<HTML>
<BODY BGCOLOR="white">
<PRE>
<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    <a name="line.17"></a>
<FONT color="green">018</FONT>    package org.apache.commons.math3.optimization.direct;<a name="line.18"></a>
<FONT color="green">019</FONT>    <a name="line.19"></a>
<FONT color="green">020</FONT>    import java.util.ArrayList;<a name="line.20"></a>
<FONT color="green">021</FONT>    import java.util.Arrays;<a name="line.21"></a>
<FONT color="green">022</FONT>    import java.util.List;<a name="line.22"></a>
<FONT color="green">023</FONT>    <a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.analysis.MultivariateFunction;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.exception.DimensionMismatchException;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math3.exception.NotPositiveException;<a name="line.26"></a>
<FONT color="green">027</FONT>    import org.apache.commons.math3.exception.NotStrictlyPositiveException;<a name="line.27"></a>
<FONT color="green">028</FONT>    import org.apache.commons.math3.exception.OutOfRangeException;<a name="line.28"></a>
<FONT color="green">029</FONT>    import org.apache.commons.math3.exception.TooManyEvaluationsException;<a name="line.29"></a>
<FONT color="green">030</FONT>    import org.apache.commons.math3.linear.Array2DRowRealMatrix;<a name="line.30"></a>
<FONT color="green">031</FONT>    import org.apache.commons.math3.linear.EigenDecomposition;<a name="line.31"></a>
<FONT color="green">032</FONT>    import org.apache.commons.math3.linear.MatrixUtils;<a name="line.32"></a>
<FONT color="green">033</FONT>    import org.apache.commons.math3.linear.RealMatrix;<a name="line.33"></a>
<FONT color="green">034</FONT>    import org.apache.commons.math3.optimization.ConvergenceChecker;<a name="line.34"></a>
<FONT color="green">035</FONT>    import org.apache.commons.math3.optimization.OptimizationData;<a name="line.35"></a>
<FONT color="green">036</FONT>    import org.apache.commons.math3.optimization.GoalType;<a name="line.36"></a>
<FONT color="green">037</FONT>    import org.apache.commons.math3.optimization.MultivariateOptimizer;<a name="line.37"></a>
<FONT color="green">038</FONT>    import org.apache.commons.math3.optimization.PointValuePair;<a name="line.38"></a>
<FONT color="green">039</FONT>    import org.apache.commons.math3.optimization.SimpleValueChecker;<a name="line.39"></a>
<FONT color="green">040</FONT>    import org.apache.commons.math3.random.MersenneTwister;<a name="line.40"></a>
<FONT color="green">041</FONT>    import org.apache.commons.math3.random.RandomGenerator;<a name="line.41"></a>
<FONT color="green">042</FONT>    import org.apache.commons.math3.util.MathArrays;<a name="line.42"></a>
<FONT color="green">043</FONT>    <a name="line.43"></a>
<FONT color="green">044</FONT>    /**<a name="line.44"></a>
<FONT color="green">045</FONT>     * &lt;p&gt;An implementation of the active Covariance Matrix Adaptation Evolution Strategy (CMA-ES)<a name="line.45"></a>
<FONT color="green">046</FONT>     * for non-linear, non-convex, non-smooth, global function minimization.<a name="line.46"></a>
<FONT color="green">047</FONT>     * The CMA-Evolution Strategy (CMA-ES) is a reliable stochastic optimization method<a name="line.47"></a>
<FONT color="green">048</FONT>     * which should be applied if derivative-based methods, e.g. quasi-Newton BFGS or<a name="line.48"></a>
<FONT color="green">049</FONT>     * conjugate gradient, fail due to a rugged search landscape (e.g. noise, local<a name="line.49"></a>
<FONT color="green">050</FONT>     * optima, outlier, etc.) of the objective function. Like a<a name="line.50"></a>
<FONT color="green">051</FONT>     * quasi-Newton method, the CMA-ES learns and applies a variable metric<a name="line.51"></a>
<FONT color="green">052</FONT>     * on the underlying search space. Unlike a quasi-Newton method, the<a name="line.52"></a>
<FONT color="green">053</FONT>     * CMA-ES neither estimates nor uses gradients, making it considerably more<a name="line.53"></a>
<FONT color="green">054</FONT>     * reliable in terms of finding a good, or even close to optimal, solution.&lt;/p&gt;<a name="line.54"></a>
<FONT color="green">055</FONT>     *<a name="line.55"></a>
<FONT color="green">056</FONT>     * &lt;p&gt;In general, on smooth objective functions the CMA-ES is roughly ten times<a name="line.56"></a>
<FONT color="green">057</FONT>     * slower than BFGS (counting objective function evaluations, no gradients provided).<a name="line.57"></a>
<FONT color="green">058</FONT>     * For up to &lt;math&gt;N=10&lt;/math&gt; variables also the derivative-free simplex<a name="line.58"></a>
<FONT color="green">059</FONT>     * direct search method (Nelder and Mead) can be faster, but it is<a name="line.59"></a>
<FONT color="green">060</FONT>     * far less reliable than CMA-ES.&lt;/p&gt;<a name="line.60"></a>
<FONT color="green">061</FONT>     *<a name="line.61"></a>
<FONT color="green">062</FONT>     * &lt;p&gt;The CMA-ES is particularly well suited for non-separable<a name="line.62"></a>
<FONT color="green">063</FONT>     * and/or badly conditioned problems. To observe the advantage of CMA compared<a name="line.63"></a>
<FONT color="green">064</FONT>     * to a conventional evolution strategy, it will usually take about<a name="line.64"></a>
<FONT color="green">065</FONT>     * &lt;math&gt;30 N&lt;/math&gt; function evaluations. On difficult problems the complete<a name="line.65"></a>
<FONT color="green">066</FONT>     * optimization (a single run) is expected to take &lt;em&gt;roughly&lt;/em&gt; between<a name="line.66"></a>
<FONT color="green">067</FONT>     * &lt;math&gt;30 N&lt;/math&gt; and &lt;math&gt;300 N&lt;sup&gt;2&lt;/sup&gt;&lt;/math&gt;<a name="line.67"></a>
<FONT color="green">068</FONT>     * function evaluations.&lt;/p&gt;<a name="line.68"></a>
<FONT color="green">069</FONT>     *<a name="line.69"></a>
<FONT color="green">070</FONT>     * &lt;p&gt;This implementation is translated and adapted from the Matlab version<a name="line.70"></a>
<FONT color="green">071</FONT>     * of the CMA-ES algorithm as implemented in module {@code cmaes.m} version 3.51.&lt;/p&gt;<a name="line.71"></a>
<FONT color="green">072</FONT>     *<a name="line.72"></a>
<FONT color="green">073</FONT>     * For more information, please refer to the following links:<a name="line.73"></a>
<FONT color="green">074</FONT>     * &lt;ul&gt;<a name="line.74"></a>
<FONT color="green">075</FONT>     *  &lt;li&gt;&lt;a href="http://www.lri.fr/~hansen/cmaes.m"&gt;Matlab code&lt;/a&gt;&lt;/li&gt;<a name="line.75"></a>
<FONT color="green">076</FONT>     *  &lt;li&gt;&lt;a href="http://www.lri.fr/~hansen/cmaesintro.html"&gt;Introduction to CMA-ES&lt;/a&gt;&lt;/li&gt;<a name="line.76"></a>
<FONT color="green">077</FONT>     *  &lt;li&gt;&lt;a href="http://en.wikipedia.org/wiki/CMA-ES"&gt;Wikipedia&lt;/a&gt;&lt;/li&gt;<a name="line.77"></a>
<FONT color="green">078</FONT>     * &lt;/ul&gt;<a name="line.78"></a>
<FONT color="green">079</FONT>     *<a name="line.79"></a>
<FONT color="green">080</FONT>     * @version $Id: CMAESOptimizer.java 1422313 2012-12-15 18:53:41Z psteitz $<a name="line.80"></a>
<FONT color="green">081</FONT>     * @deprecated As of 3.1 (to be removed in 4.0).<a name="line.81"></a>
<FONT color="green">082</FONT>     * @since 3.0<a name="line.82"></a>
<FONT color="green">083</FONT>     */<a name="line.83"></a>
<FONT color="green">084</FONT>    <a name="line.84"></a>
<FONT color="green">085</FONT>    @Deprecated<a name="line.85"></a>
<FONT color="green">086</FONT>    public class CMAESOptimizer<a name="line.86"></a>
<FONT color="green">087</FONT>        extends BaseAbstractMultivariateSimpleBoundsOptimizer&lt;MultivariateFunction&gt;<a name="line.87"></a>
<FONT color="green">088</FONT>        implements MultivariateOptimizer {<a name="line.88"></a>
<FONT color="green">089</FONT>        /** Default value for {@link #checkFeasableCount}: {@value}. */<a name="line.89"></a>
<FONT color="green">090</FONT>        public static final int DEFAULT_CHECKFEASABLECOUNT = 0;<a name="line.90"></a>
<FONT color="green">091</FONT>        /** Default value for {@link #stopFitness}: {@value}. */<a name="line.91"></a>
<FONT color="green">092</FONT>        public static final double DEFAULT_STOPFITNESS = 0;<a name="line.92"></a>
<FONT color="green">093</FONT>        /** Default value for {@link #isActiveCMA}: {@value}. */<a name="line.93"></a>
<FONT color="green">094</FONT>        public static final boolean DEFAULT_ISACTIVECMA = true;<a name="line.94"></a>
<FONT color="green">095</FONT>        /** Default value for {@link #maxIterations}: {@value}. */<a name="line.95"></a>
<FONT color="green">096</FONT>        public static final int DEFAULT_MAXITERATIONS = 30000;<a name="line.96"></a>
<FONT color="green">097</FONT>        /** Default value for {@link #diagonalOnly}: {@value}. */<a name="line.97"></a>
<FONT color="green">098</FONT>        public static final int DEFAULT_DIAGONALONLY = 0;<a name="line.98"></a>
<FONT color="green">099</FONT>        /** Default value for {@link #random}. */<a name="line.99"></a>
<FONT color="green">100</FONT>        public static final RandomGenerator DEFAULT_RANDOMGENERATOR = new MersenneTwister();<a name="line.100"></a>
<FONT color="green">101</FONT>    <a name="line.101"></a>
<FONT color="green">102</FONT>        // global search parameters<a name="line.102"></a>
<FONT color="green">103</FONT>        /**<a name="line.103"></a>
<FONT color="green">104</FONT>         * Population size, offspring number. The primary strategy parameter to play<a name="line.104"></a>
<FONT color="green">105</FONT>         * with, which can be increased from its default value. Increasing the<a name="line.105"></a>
<FONT color="green">106</FONT>         * population size improves global search properties in exchange to speed.<a name="line.106"></a>
<FONT color="green">107</FONT>         * Speed decreases, as a rule, at most linearly with increasing population<a name="line.107"></a>
<FONT color="green">108</FONT>         * size. It is advisable to begin with the default small population size.<a name="line.108"></a>
<FONT color="green">109</FONT>         */<a name="line.109"></a>
<FONT color="green">110</FONT>        private int lambda; // population size<a name="line.110"></a>
<FONT color="green">111</FONT>        /**<a name="line.111"></a>
<FONT color="green">112</FONT>         * Covariance update mechanism, default is active CMA. isActiveCMA = true<a name="line.112"></a>
<FONT color="green">113</FONT>         * turns on "active CMA" with a negative update of the covariance matrix and<a name="line.113"></a>
<FONT color="green">114</FONT>         * checks for positive definiteness. OPTS.CMA.active = 2 does not check for<a name="line.114"></a>
<FONT color="green">115</FONT>         * pos. def. and is numerically faster. Active CMA usually speeds up the<a name="line.115"></a>
<FONT color="green">116</FONT>         * adaptation.<a name="line.116"></a>
<FONT color="green">117</FONT>         */<a name="line.117"></a>
<FONT color="green">118</FONT>        private boolean isActiveCMA;<a name="line.118"></a>
<FONT color="green">119</FONT>        /**<a name="line.119"></a>
<FONT color="green">120</FONT>         * Determines how often a new random offspring is generated in case it is<a name="line.120"></a>
<FONT color="green">121</FONT>         * not feasible / beyond the defined limits, default is 0.<a name="line.121"></a>
<FONT color="green">122</FONT>         */<a name="line.122"></a>
<FONT color="green">123</FONT>        private int checkFeasableCount;<a name="line.123"></a>
<FONT color="green">124</FONT>        /**<a name="line.124"></a>
<FONT color="green">125</FONT>         * @see Sigma<a name="line.125"></a>
<FONT color="green">126</FONT>         */<a name="line.126"></a>
<FONT color="green">127</FONT>        private double[] inputSigma;<a name="line.127"></a>
<FONT color="green">128</FONT>        /** Number of objective variables/problem dimension */<a name="line.128"></a>
<FONT color="green">129</FONT>        private int dimension;<a name="line.129"></a>
<FONT color="green">130</FONT>        /**<a name="line.130"></a>
<FONT color="green">131</FONT>         * Defines the number of initial iterations, where the covariance matrix<a name="line.131"></a>
<FONT color="green">132</FONT>         * remains diagonal and the algorithm has internally linear time complexity.<a name="line.132"></a>
<FONT color="green">133</FONT>         * diagonalOnly = 1 means keeping the covariance matrix always diagonal and<a name="line.133"></a>
<FONT color="green">134</FONT>         * this setting also exhibits linear space complexity. This can be<a name="line.134"></a>
<FONT color="green">135</FONT>         * particularly useful for dimension &gt; 100.<a name="line.135"></a>
<FONT color="green">136</FONT>         * @see &lt;a href="http://hal.archives-ouvertes.fr/inria-00287367/en"&gt;A Simple Modification in CMA-ES&lt;/a&gt;<a name="line.136"></a>
<FONT color="green">137</FONT>         */<a name="line.137"></a>
<FONT color="green">138</FONT>        private int diagonalOnly = 0;<a name="line.138"></a>
<FONT color="green">139</FONT>        /** Number of objective variables/problem dimension */<a name="line.139"></a>
<FONT color="green">140</FONT>        private boolean isMinimize = true;<a name="line.140"></a>
<FONT color="green">141</FONT>        /** Indicates whether statistic data is collected. */<a name="line.141"></a>
<FONT color="green">142</FONT>        private boolean generateStatistics = false;<a name="line.142"></a>
<FONT color="green">143</FONT>    <a name="line.143"></a>
<FONT color="green">144</FONT>        // termination criteria<a name="line.144"></a>
<FONT color="green">145</FONT>        /** Maximal number of iterations allowed. */<a name="line.145"></a>
<FONT color="green">146</FONT>        private int maxIterations;<a name="line.146"></a>
<FONT color="green">147</FONT>        /** Limit for fitness value. */<a name="line.147"></a>
<FONT color="green">148</FONT>        private double stopFitness;<a name="line.148"></a>
<FONT color="green">149</FONT>        /** Stop if x-changes larger stopTolUpX. */<a name="line.149"></a>
<FONT color="green">150</FONT>        private double stopTolUpX;<a name="line.150"></a>
<FONT color="green">151</FONT>        /** Stop if x-change smaller stopTolX. */<a name="line.151"></a>
<FONT color="green">152</FONT>        private double stopTolX;<a name="line.152"></a>
<FONT color="green">153</FONT>        /** Stop if fun-changes smaller stopTolFun. */<a name="line.153"></a>
<FONT color="green">154</FONT>        private double stopTolFun;<a name="line.154"></a>
<FONT color="green">155</FONT>        /** Stop if back fun-changes smaller stopTolHistFun. */<a name="line.155"></a>
<FONT color="green">156</FONT>        private double stopTolHistFun;<a name="line.156"></a>
<FONT color="green">157</FONT>    <a name="line.157"></a>
<FONT color="green">158</FONT>        // selection strategy parameters<a name="line.158"></a>
<FONT color="green">159</FONT>        /** Number of parents/points for recombination. */<a name="line.159"></a>
<FONT color="green">160</FONT>        private int mu; //<a name="line.160"></a>
<FONT color="green">161</FONT>        /** log(mu + 0.5), stored for efficiency. */<a name="line.161"></a>
<FONT color="green">162</FONT>        private double logMu2;<a name="line.162"></a>
<FONT color="green">163</FONT>        /** Array for weighted recombination. */<a name="line.163"></a>
<FONT color="green">164</FONT>        private RealMatrix weights;<a name="line.164"></a>
<FONT color="green">165</FONT>        /** Variance-effectiveness of sum w_i x_i. */<a name="line.165"></a>
<FONT color="green">166</FONT>        private double mueff; //<a name="line.166"></a>
<FONT color="green">167</FONT>    <a name="line.167"></a>
<FONT color="green">168</FONT>        // dynamic strategy parameters and constants<a name="line.168"></a>
<FONT color="green">169</FONT>        /** Overall standard deviation - search volume. */<a name="line.169"></a>
<FONT color="green">170</FONT>        private double sigma;<a name="line.170"></a>
<FONT color="green">171</FONT>        /** Cumulation constant. */<a name="line.171"></a>
<FONT color="green">172</FONT>        private double cc;<a name="line.172"></a>
<FONT color="green">173</FONT>        /** Cumulation constant for step-size. */<a name="line.173"></a>
<FONT color="green">174</FONT>        private double cs;<a name="line.174"></a>
<FONT color="green">175</FONT>        /** Damping for step-size. */<a name="line.175"></a>
<FONT color="green">176</FONT>        private double damps;<a name="line.176"></a>
<FONT color="green">177</FONT>        /** Learning rate for rank-one update. */<a name="line.177"></a>
<FONT color="green">178</FONT>        private double ccov1;<a name="line.178"></a>
<FONT color="green">179</FONT>        /** Learning rate for rank-mu update' */<a name="line.179"></a>
<FONT color="green">180</FONT>        private double ccovmu;<a name="line.180"></a>
<FONT color="green">181</FONT>        /** Expectation of ||N(0,I)|| == norm(randn(N,1)). */<a name="line.181"></a>
<FONT color="green">182</FONT>        private double chiN;<a name="line.182"></a>
<FONT color="green">183</FONT>        /** Learning rate for rank-one update - diagonalOnly */<a name="line.183"></a>
<FONT color="green">184</FONT>        private double ccov1Sep;<a name="line.184"></a>
<FONT color="green">185</FONT>        /** Learning rate for rank-mu update - diagonalOnly */<a name="line.185"></a>
<FONT color="green">186</FONT>        private double ccovmuSep;<a name="line.186"></a>
<FONT color="green">187</FONT>    <a name="line.187"></a>
<FONT color="green">188</FONT>        // CMA internal values - updated each generation<a name="line.188"></a>
<FONT color="green">189</FONT>        /** Objective variables. */<a name="line.189"></a>
<FONT color="green">190</FONT>        private RealMatrix xmean;<a name="line.190"></a>
<FONT color="green">191</FONT>        /** Evolution path. */<a name="line.191"></a>
<FONT color="green">192</FONT>        private RealMatrix pc;<a name="line.192"></a>
<FONT color="green">193</FONT>        /** Evolution path for sigma. */<a name="line.193"></a>
<FONT color="green">194</FONT>        private RealMatrix ps;<a name="line.194"></a>
<FONT color="green">195</FONT>        /** Norm of ps, stored for efficiency. */<a name="line.195"></a>
<FONT color="green">196</FONT>        private double normps;<a name="line.196"></a>
<FONT color="green">197</FONT>        /** Coordinate system. */<a name="line.197"></a>
<FONT color="green">198</FONT>        private RealMatrix B;<a name="line.198"></a>
<FONT color="green">199</FONT>        /** Scaling. */<a name="line.199"></a>
<FONT color="green">200</FONT>        private RealMatrix D;<a name="line.200"></a>
<FONT color="green">201</FONT>        /** B*D, stored for efficiency. */<a name="line.201"></a>
<FONT color="green">202</FONT>        private RealMatrix BD;<a name="line.202"></a>
<FONT color="green">203</FONT>        /** Diagonal of sqrt(D), stored for efficiency. */<a name="line.203"></a>
<FONT color="green">204</FONT>        private RealMatrix diagD;<a name="line.204"></a>
<FONT color="green">205</FONT>        /** Covariance matrix. */<a name="line.205"></a>
<FONT color="green">206</FONT>        private RealMatrix C;<a name="line.206"></a>
<FONT color="green">207</FONT>        /** Diagonal of C, used for diagonalOnly. */<a name="line.207"></a>
<FONT color="green">208</FONT>        private RealMatrix diagC;<a name="line.208"></a>
<FONT color="green">209</FONT>        /** Number of iterations already performed. */<a name="line.209"></a>
<FONT color="green">210</FONT>        private int iterations;<a name="line.210"></a>
<FONT color="green">211</FONT>    <a name="line.211"></a>
<FONT color="green">212</FONT>        /** History queue of best values. */<a name="line.212"></a>
<FONT color="green">213</FONT>        private double[] fitnessHistory;<a name="line.213"></a>
<FONT color="green">214</FONT>        /** Size of history queue of best values. */<a name="line.214"></a>
<FONT color="green">215</FONT>        private int historySize;<a name="line.215"></a>
<FONT color="green">216</FONT>    <a name="line.216"></a>
<FONT color="green">217</FONT>        /** Random generator. */<a name="line.217"></a>
<FONT color="green">218</FONT>        private RandomGenerator random;<a name="line.218"></a>
<FONT color="green">219</FONT>    <a name="line.219"></a>
<FONT color="green">220</FONT>        /** History of sigma values. */<a name="line.220"></a>
<FONT color="green">221</FONT>        private List&lt;Double&gt; statisticsSigmaHistory = new ArrayList&lt;Double&gt;();<a name="line.221"></a>
<FONT color="green">222</FONT>        /** History of mean matrix. */<a name="line.222"></a>
<FONT color="green">223</FONT>        private List&lt;RealMatrix&gt; statisticsMeanHistory = new ArrayList&lt;RealMatrix&gt;();<a name="line.223"></a>
<FONT color="green">224</FONT>        /** History of fitness values. */<a name="line.224"></a>
<FONT color="green">225</FONT>        private List&lt;Double&gt; statisticsFitnessHistory = new ArrayList&lt;Double&gt;();<a name="line.225"></a>
<FONT color="green">226</FONT>        /** History of D matrix. */<a name="line.226"></a>
<FONT color="green">227</FONT>        private List&lt;RealMatrix&gt; statisticsDHistory = new ArrayList&lt;RealMatrix&gt;();<a name="line.227"></a>
<FONT color="green">228</FONT>    <a name="line.228"></a>
<FONT color="green">229</FONT>        /**<a name="line.229"></a>
<FONT color="green">230</FONT>         * Default constructor, uses default parameters<a name="line.230"></a>
<FONT color="green">231</FONT>         *<a name="line.231"></a>
<FONT color="green">232</FONT>         * @deprecated As of version 3.1: Parameter {@code lambda} must be<a name="line.232"></a>
<FONT color="green">233</FONT>         * passed with the call to {@link #optimize(int,MultivariateFunction,GoalType,OptimizationData[])<a name="line.233"></a>
<FONT color="green">234</FONT>         * optimize} (whereas in the current code it is set to an undocumented value).<a name="line.234"></a>
<FONT color="green">235</FONT>         */<a name="line.235"></a>
<FONT color="green">236</FONT>        public CMAESOptimizer() {<a name="line.236"></a>
<FONT color="green">237</FONT>            this(0);<a name="line.237"></a>
<FONT color="green">238</FONT>        }<a name="line.238"></a>
<FONT color="green">239</FONT>    <a name="line.239"></a>
<FONT color="green">240</FONT>        /**<a name="line.240"></a>
<FONT color="green">241</FONT>         * @param lambda Population size.<a name="line.241"></a>
<FONT color="green">242</FONT>         * @deprecated As of version 3.1: Parameter {@code lambda} must be<a name="line.242"></a>
<FONT color="green">243</FONT>         * passed with the call to {@link #optimize(int,MultivariateFunction,GoalType,OptimizationData[])<a name="line.243"></a>
<FONT color="green">244</FONT>         * optimize} (whereas in the current code it is set to an undocumented value)..<a name="line.244"></a>
<FONT color="green">245</FONT>         */<a name="line.245"></a>
<FONT color="green">246</FONT>        public CMAESOptimizer(int lambda) {<a name="line.246"></a>
<FONT color="green">247</FONT>            this(lambda, null, DEFAULT_MAXITERATIONS, DEFAULT_STOPFITNESS,<a name="line.247"></a>
<FONT color="green">248</FONT>                 DEFAULT_ISACTIVECMA, DEFAULT_DIAGONALONLY,<a name="line.248"></a>
<FONT color="green">249</FONT>                 DEFAULT_CHECKFEASABLECOUNT, DEFAULT_RANDOMGENERATOR,<a name="line.249"></a>
<FONT color="green">250</FONT>                 false, null);<a name="line.250"></a>
<FONT color="green">251</FONT>        }<a name="line.251"></a>
<FONT color="green">252</FONT>    <a name="line.252"></a>
<FONT color="green">253</FONT>        /**<a name="line.253"></a>
<FONT color="green">254</FONT>         * @param lambda Population size.<a name="line.254"></a>
<FONT color="green">255</FONT>         * @param inputSigma Initial standard deviations to sample new points<a name="line.255"></a>
<FONT color="green">256</FONT>         * around the initial guess.<a name="line.256"></a>
<FONT color="green">257</FONT>         * @deprecated As of version 3.1: Parameters {@code lambda} and {@code inputSigma} must be<a name="line.257"></a>
<FONT color="green">258</FONT>         * passed with the call to {@link #optimize(int,MultivariateFunction,GoalType,OptimizationData[])<a name="line.258"></a>
<FONT color="green">259</FONT>         * optimize}.<a name="line.259"></a>
<FONT color="green">260</FONT>         */<a name="line.260"></a>
<FONT color="green">261</FONT>        @Deprecated<a name="line.261"></a>
<FONT color="green">262</FONT>        public CMAESOptimizer(int lambda, double[] inputSigma) {<a name="line.262"></a>
<FONT color="green">263</FONT>            this(lambda, inputSigma, DEFAULT_MAXITERATIONS, DEFAULT_STOPFITNESS,<a name="line.263"></a>
<FONT color="green">264</FONT>                 DEFAULT_ISACTIVECMA, DEFAULT_DIAGONALONLY,<a name="line.264"></a>
<FONT color="green">265</FONT>                 DEFAULT_CHECKFEASABLECOUNT, DEFAULT_RANDOMGENERATOR, false);<a name="line.265"></a>
<FONT color="green">266</FONT>        }<a name="line.266"></a>
<FONT color="green">267</FONT>    <a name="line.267"></a>
<FONT color="green">268</FONT>        /**<a name="line.268"></a>
<FONT color="green">269</FONT>         * @param lambda Population size.<a name="line.269"></a>
<FONT color="green">270</FONT>         * @param inputSigma Initial standard deviations to sample new points<a name="line.270"></a>
<FONT color="green">271</FONT>         * around the initial guess.<a name="line.271"></a>
<FONT color="green">272</FONT>         * @param maxIterations Maximal number of iterations.<a name="line.272"></a>
<FONT color="green">273</FONT>         * @param stopFitness Whether to stop if objective function value is smaller than<a name="line.273"></a>
<FONT color="green">274</FONT>         * {@code stopFitness}.<a name="line.274"></a>
<FONT color="green">275</FONT>         * @param isActiveCMA Chooses the covariance matrix update method.<a name="line.275"></a>
<FONT color="green">276</FONT>         * @param diagonalOnly Number of initial iterations, where the covariance matrix<a name="line.276"></a>
<FONT color="green">277</FONT>         * remains diagonal.<a name="line.277"></a>
<FONT color="green">278</FONT>         * @param checkFeasableCount Determines how often new random objective variables are<a name="line.278"></a>
<FONT color="green">279</FONT>         * generated in case they are out of bounds.<a name="line.279"></a>
<FONT color="green">280</FONT>         * @param random Random generator.<a name="line.280"></a>
<FONT color="green">281</FONT>         * @param generateStatistics Whether statistic data is collected.<a name="line.281"></a>
<FONT color="green">282</FONT>         * @deprecated See {@link SimpleValueChecker#SimpleValueChecker()}<a name="line.282"></a>
<FONT color="green">283</FONT>         */<a name="line.283"></a>
<FONT color="green">284</FONT>        @Deprecated<a name="line.284"></a>
<FONT color="green">285</FONT>        public CMAESOptimizer(int lambda, double[] inputSigma,<a name="line.285"></a>
<FONT color="green">286</FONT>                              int maxIterations, double stopFitness,<a name="line.286"></a>
<FONT color="green">287</FONT>                              boolean isActiveCMA, int diagonalOnly, int checkFeasableCount,<a name="line.287"></a>
<FONT color="green">288</FONT>                              RandomGenerator random, boolean generateStatistics) {<a name="line.288"></a>
<FONT color="green">289</FONT>            this(lambda, inputSigma, maxIterations, stopFitness, isActiveCMA,<a name="line.289"></a>
<FONT color="green">290</FONT>                 diagonalOnly, checkFeasableCount, random, generateStatistics,<a name="line.290"></a>
<FONT color="green">291</FONT>                 new SimpleValueChecker());<a name="line.291"></a>
<FONT color="green">292</FONT>        }<a name="line.292"></a>
<FONT color="green">293</FONT>    <a name="line.293"></a>
<FONT color="green">294</FONT>        /**<a name="line.294"></a>
<FONT color="green">295</FONT>         * @param lambda Population size.<a name="line.295"></a>
<FONT color="green">296</FONT>         * @param inputSigma Initial standard deviations to sample new points<a name="line.296"></a>
<FONT color="green">297</FONT>         * around the initial guess.<a name="line.297"></a>
<FONT color="green">298</FONT>         * @param maxIterations Maximal number of iterations.<a name="line.298"></a>
<FONT color="green">299</FONT>         * @param stopFitness Whether to stop if objective function value is smaller than<a name="line.299"></a>
<FONT color="green">300</FONT>         * {@code stopFitness}.<a name="line.300"></a>
<FONT color="green">301</FONT>         * @param isActiveCMA Chooses the covariance matrix update method.<a name="line.301"></a>
<FONT color="green">302</FONT>         * @param diagonalOnly Number of initial iterations, where the covariance matrix<a name="line.302"></a>
<FONT color="green">303</FONT>         * remains diagonal.<a name="line.303"></a>
<FONT color="green">304</FONT>         * @param checkFeasableCount Determines how often new random objective variables are<a name="line.304"></a>
<FONT color="green">305</FONT>         * generated in case they are out of bounds.<a name="line.305"></a>
<FONT color="green">306</FONT>         * @param random Random generator.<a name="line.306"></a>
<FONT color="green">307</FONT>         * @param generateStatistics Whether statistic data is collected.<a name="line.307"></a>
<FONT color="green">308</FONT>         * @param checker Convergence checker.<a name="line.308"></a>
<FONT color="green">309</FONT>         * @deprecated As of version 3.1: Parameters {@code lambda} and {@code inputSigma} must be<a name="line.309"></a>
<FONT color="green">310</FONT>         * passed with the call to {@link #optimize(int,MultivariateFunction,GoalType,OptimizationData[])<a name="line.310"></a>
<FONT color="green">311</FONT>         * optimize}.<a name="line.311"></a>
<FONT color="green">312</FONT>         */<a name="line.312"></a>
<FONT color="green">313</FONT>        @Deprecated<a name="line.313"></a>
<FONT color="green">314</FONT>        public CMAESOptimizer(int lambda, double[] inputSigma,<a name="line.314"></a>
<FONT color="green">315</FONT>                              int maxIterations, double stopFitness,<a name="line.315"></a>
<FONT color="green">316</FONT>                              boolean isActiveCMA, int diagonalOnly, int checkFeasableCount,<a name="line.316"></a>
<FONT color="green">317</FONT>                              RandomGenerator random, boolean generateStatistics,<a name="line.317"></a>
<FONT color="green">318</FONT>                              ConvergenceChecker&lt;PointValuePair&gt; checker) {<a name="line.318"></a>
<FONT color="green">319</FONT>            super(checker);<a name="line.319"></a>
<FONT color="green">320</FONT>            this.lambda = lambda;<a name="line.320"></a>
<FONT color="green">321</FONT>            this.inputSigma = inputSigma == null ? null : (double[]) inputSigma.clone();<a name="line.321"></a>
<FONT color="green">322</FONT>            this.maxIterations = maxIterations;<a name="line.322"></a>
<FONT color="green">323</FONT>            this.stopFitness = stopFitness;<a name="line.323"></a>
<FONT color="green">324</FONT>            this.isActiveCMA = isActiveCMA;<a name="line.324"></a>
<FONT color="green">325</FONT>            this.diagonalOnly = diagonalOnly;<a name="line.325"></a>
<FONT color="green">326</FONT>            this.checkFeasableCount = checkFeasableCount;<a name="line.326"></a>
<FONT color="green">327</FONT>            this.random = random;<a name="line.327"></a>
<FONT color="green">328</FONT>            this.generateStatistics = generateStatistics;<a name="line.328"></a>
<FONT color="green">329</FONT>        }<a name="line.329"></a>
<FONT color="green">330</FONT>    <a name="line.330"></a>
<FONT color="green">331</FONT>        /**<a name="line.331"></a>
<FONT color="green">332</FONT>         * @param maxIterations Maximal number of iterations.<a name="line.332"></a>
<FONT color="green">333</FONT>         * @param stopFitness Whether to stop if objective function value is smaller than<a name="line.333"></a>
<FONT color="green">334</FONT>         * {@code stopFitness}.<a name="line.334"></a>
<FONT color="green">335</FONT>         * @param isActiveCMA Chooses the covariance matrix update method.<a name="line.335"></a>
<FONT color="green">336</FONT>         * @param diagonalOnly Number of initial iterations, where the covariance matrix<a name="line.336"></a>
<FONT color="green">337</FONT>         * remains diagonal.<a name="line.337"></a>
<FONT color="green">338</FONT>         * @param checkFeasableCount Determines how often new random objective variables are<a name="line.338"></a>
<FONT color="green">339</FONT>         * generated in case they are out of bounds.<a name="line.339"></a>
<FONT color="green">340</FONT>         * @param random Random generator.<a name="line.340"></a>
<FONT color="green">341</FONT>         * @param generateStatistics Whether statistic data is collected.<a name="line.341"></a>
<FONT color="green">342</FONT>         * @param checker Convergence checker.<a name="line.342"></a>
<FONT color="green">343</FONT>         *<a name="line.343"></a>
<FONT color="green">344</FONT>         * @since 3.1<a name="line.344"></a>
<FONT color="green">345</FONT>         */<a name="line.345"></a>
<FONT color="green">346</FONT>        public CMAESOptimizer(int maxIterations,<a name="line.346"></a>
<FONT color="green">347</FONT>                              double stopFitness,<a name="line.347"></a>
<FONT color="green">348</FONT>                              boolean isActiveCMA,<a name="line.348"></a>
<FONT color="green">349</FONT>                              int diagonalOnly,<a name="line.349"></a>
<FONT color="green">350</FONT>                              int checkFeasableCount,<a name="line.350"></a>
<FONT color="green">351</FONT>                              RandomGenerator random,<a name="line.351"></a>
<FONT color="green">352</FONT>                              boolean generateStatistics,<a name="line.352"></a>
<FONT color="green">353</FONT>                              ConvergenceChecker&lt;PointValuePair&gt; checker) {<a name="line.353"></a>
<FONT color="green">354</FONT>            super(checker);<a name="line.354"></a>
<FONT color="green">355</FONT>            this.maxIterations = maxIterations;<a name="line.355"></a>
<FONT color="green">356</FONT>            this.stopFitness = stopFitness;<a name="line.356"></a>
<FONT color="green">357</FONT>            this.isActiveCMA = isActiveCMA;<a name="line.357"></a>
<FONT color="green">358</FONT>            this.diagonalOnly = diagonalOnly;<a name="line.358"></a>
<FONT color="green">359</FONT>            this.checkFeasableCount = checkFeasableCount;<a name="line.359"></a>
<FONT color="green">360</FONT>            this.random = random;<a name="line.360"></a>
<FONT color="green">361</FONT>            this.generateStatistics = generateStatistics;<a name="line.361"></a>
<FONT color="green">362</FONT>        }<a name="line.362"></a>
<FONT color="green">363</FONT>    <a name="line.363"></a>
<FONT color="green">364</FONT>        /**<a name="line.364"></a>
<FONT color="green">365</FONT>         * @return History of sigma values.<a name="line.365"></a>
<FONT color="green">366</FONT>         */<a name="line.366"></a>
<FONT color="green">367</FONT>        public List&lt;Double&gt; getStatisticsSigmaHistory() {<a name="line.367"></a>
<FONT color="green">368</FONT>            return statisticsSigmaHistory;<a name="line.368"></a>
<FONT color="green">369</FONT>        }<a name="line.369"></a>
<FONT color="green">370</FONT>    <a name="line.370"></a>
<FONT color="green">371</FONT>        /**<a name="line.371"></a>
<FONT color="green">372</FONT>         * @return History of mean matrix.<a name="line.372"></a>
<FONT color="green">373</FONT>         */<a name="line.373"></a>
<FONT color="green">374</FONT>        public List&lt;RealMatrix&gt; getStatisticsMeanHistory() {<a name="line.374"></a>
<FONT color="green">375</FONT>            return statisticsMeanHistory;<a name="line.375"></a>
<FONT color="green">376</FONT>        }<a name="line.376"></a>
<FONT color="green">377</FONT>    <a name="line.377"></a>
<FONT color="green">378</FONT>        /**<a name="line.378"></a>
<FONT color="green">379</FONT>         * @return History of fitness values.<a name="line.379"></a>
<FONT color="green">380</FONT>         */<a name="line.380"></a>
<FONT color="green">381</FONT>        public List&lt;Double&gt; getStatisticsFitnessHistory() {<a name="line.381"></a>
<FONT color="green">382</FONT>            return statisticsFitnessHistory;<a name="line.382"></a>
<FONT color="green">383</FONT>        }<a name="line.383"></a>
<FONT color="green">384</FONT>    <a name="line.384"></a>
<FONT color="green">385</FONT>        /**<a name="line.385"></a>
<FONT color="green">386</FONT>         * @return History of D matrix.<a name="line.386"></a>
<FONT color="green">387</FONT>         */<a name="line.387"></a>
<FONT color="green">388</FONT>        public List&lt;RealMatrix&gt; getStatisticsDHistory() {<a name="line.388"></a>
<FONT color="green">389</FONT>            return statisticsDHistory;<a name="line.389"></a>
<FONT color="green">390</FONT>        }<a name="line.390"></a>
<FONT color="green">391</FONT>    <a name="line.391"></a>
<FONT color="green">392</FONT>        /**<a name="line.392"></a>
<FONT color="green">393</FONT>         * Input sigma values.<a name="line.393"></a>
<FONT color="green">394</FONT>         * They define the initial coordinate-wise standard deviations for<a name="line.394"></a>
<FONT color="green">395</FONT>         * sampling new search points around the initial guess.<a name="line.395"></a>
<FONT color="green">396</FONT>         * It is suggested to set them to the estimated distance from the<a name="line.396"></a>
<FONT color="green">397</FONT>         * initial to the desired optimum.<a name="line.397"></a>
<FONT color="green">398</FONT>         * Small values induce the search to be more local (and very small<a name="line.398"></a>
<FONT color="green">399</FONT>         * values are more likely to find a local optimum close to the initial<a name="line.399"></a>
<FONT color="green">400</FONT>         * guess).<a name="line.400"></a>
<FONT color="green">401</FONT>         * Too small values might however lead to early termination.<a name="line.401"></a>
<FONT color="green">402</FONT>         * @since 3.1<a name="line.402"></a>
<FONT color="green">403</FONT>         */<a name="line.403"></a>
<FONT color="green">404</FONT>        public static class Sigma implements OptimizationData {<a name="line.404"></a>
<FONT color="green">405</FONT>            /** Sigma values. */<a name="line.405"></a>
<FONT color="green">406</FONT>            private final double[] sigma;<a name="line.406"></a>
<FONT color="green">407</FONT>    <a name="line.407"></a>
<FONT color="green">408</FONT>            /**<a name="line.408"></a>
<FONT color="green">409</FONT>             * @param s Sigma values.<a name="line.409"></a>
<FONT color="green">410</FONT>             * @throws NotPositiveException if any of the array entries is smaller<a name="line.410"></a>
<FONT color="green">411</FONT>             * than zero.<a name="line.411"></a>
<FONT color="green">412</FONT>             */<a name="line.412"></a>
<FONT color="green">413</FONT>            public Sigma(double[] s)<a name="line.413"></a>
<FONT color="green">414</FONT>                throws NotPositiveException {<a name="line.414"></a>
<FONT color="green">415</FONT>                for (int i = 0; i &lt; s.length; i++) {<a name="line.415"></a>
<FONT color="green">416</FONT>                    if (s[i] &lt; 0) {<a name="line.416"></a>
<FONT color="green">417</FONT>                        throw new NotPositiveException(s[i]);<a name="line.417"></a>
<FONT color="green">418</FONT>                    }<a name="line.418"></a>
<FONT color="green">419</FONT>                }<a name="line.419"></a>
<FONT color="green">420</FONT>    <a name="line.420"></a>
<FONT color="green">421</FONT>                sigma = s.clone();<a name="line.421"></a>
<FONT color="green">422</FONT>            }<a name="line.422"></a>
<FONT color="green">423</FONT>    <a name="line.423"></a>
<FONT color="green">424</FONT>            /**<a name="line.424"></a>
<FONT color="green">425</FONT>             * @return the sigma values.<a name="line.425"></a>
<FONT color="green">426</FONT>             */<a name="line.426"></a>
<FONT color="green">427</FONT>            public double[] getSigma() {<a name="line.427"></a>
<FONT color="green">428</FONT>                return sigma.clone();<a name="line.428"></a>
<FONT color="green">429</FONT>            }<a name="line.429"></a>
<FONT color="green">430</FONT>        }<a name="line.430"></a>
<FONT color="green">431</FONT>    <a name="line.431"></a>
<FONT color="green">432</FONT>        /**<a name="line.432"></a>
<FONT color="green">433</FONT>         * Population size.<a name="line.433"></a>
<FONT color="green">434</FONT>         * The number of offspring is the primary strategy parameter.<a name="line.434"></a>
<FONT color="green">435</FONT>         * In the absence of better clues, a good default could be an<a name="line.435"></a>
<FONT color="green">436</FONT>         * integer close to {@code 4 + 3 ln(n)}, where {@code n} is the<a name="line.436"></a>
<FONT color="green">437</FONT>         * number of optimized parameters.<a name="line.437"></a>
<FONT color="green">438</FONT>         * Increasing the population size improves global search properties<a name="line.438"></a>
<FONT color="green">439</FONT>         * at the expense of speed (which in general decreases at most<a name="line.439"></a>
<FONT color="green">440</FONT>         * linearly with increasing population size).<a name="line.440"></a>
<FONT color="green">441</FONT>         * @since 3.1<a name="line.441"></a>
<FONT color="green">442</FONT>         */<a name="line.442"></a>
<FONT color="green">443</FONT>        public static class PopulationSize implements OptimizationData {<a name="line.443"></a>
<FONT color="green">444</FONT>            /** Population size. */<a name="line.444"></a>
<FONT color="green">445</FONT>            private final int lambda;<a name="line.445"></a>
<FONT color="green">446</FONT>    <a name="line.446"></a>
<FONT color="green">447</FONT>            /**<a name="line.447"></a>
<FONT color="green">448</FONT>             * @param size Population size.<a name="line.448"></a>
<FONT color="green">449</FONT>             * @throws NotStrictlyPositiveException if {@code size &lt;= 0}.<a name="line.449"></a>
<FONT color="green">450</FONT>             */<a name="line.450"></a>
<FONT color="green">451</FONT>            public PopulationSize(int size)<a name="line.451"></a>
<FONT color="green">452</FONT>                throws NotStrictlyPositiveException {<a name="line.452"></a>
<FONT color="green">453</FONT>                if (size &lt;= 0) {<a name="line.453"></a>
<FONT color="green">454</FONT>                    throw new NotStrictlyPositiveException(size);<a name="line.454"></a>
<FONT color="green">455</FONT>                }<a name="line.455"></a>
<FONT color="green">456</FONT>                lambda = size;<a name="line.456"></a>
<FONT color="green">457</FONT>            }<a name="line.457"></a>
<FONT color="green">458</FONT>    <a name="line.458"></a>
<FONT color="green">459</FONT>            /**<a name="line.459"></a>
<FONT color="green">460</FONT>             * @return the population size.<a name="line.460"></a>
<FONT color="green">461</FONT>             */<a name="line.461"></a>
<FONT color="green">462</FONT>            public int getPopulationSize() {<a name="line.462"></a>
<FONT color="green">463</FONT>                return lambda;<a name="line.463"></a>
<FONT color="green">464</FONT>            }<a name="line.464"></a>
<FONT color="green">465</FONT>        }<a name="line.465"></a>
<FONT color="green">466</FONT>    <a name="line.466"></a>
<FONT color="green">467</FONT>        /**<a name="line.467"></a>
<FONT color="green">468</FONT>         * Optimize an objective function.<a name="line.468"></a>
<FONT color="green">469</FONT>         *<a name="line.469"></a>
<FONT color="green">470</FONT>         * @param maxEval Allowed number of evaluations of the objective function.<a name="line.470"></a>
<FONT color="green">471</FONT>         * @param f Objective function.<a name="line.471"></a>
<FONT color="green">472</FONT>         * @param goalType Optimization type.<a name="line.472"></a>
<FONT color="green">473</FONT>         * @param optData Optimization data. The following data will be looked for:<a name="line.473"></a>
<FONT color="green">474</FONT>         * &lt;ul&gt;<a name="line.474"></a>
<FONT color="green">475</FONT>         *  &lt;li&gt;{@link org.apache.commons.math3.optimization.InitialGuess InitialGuess}&lt;/li&gt;<a name="line.475"></a>
<FONT color="green">476</FONT>         *  &lt;li&gt;{@link Sigma}&lt;/li&gt;<a name="line.476"></a>
<FONT color="green">477</FONT>         *  &lt;li&gt;{@link PopulationSize}&lt;/li&gt;<a name="line.477"></a>
<FONT color="green">478</FONT>         * &lt;/ul&gt;<a name="line.478"></a>
<FONT color="green">479</FONT>         * @return the point/value pair giving the optimal value for objective<a name="line.479"></a>
<FONT color="green">480</FONT>         * function.<a name="line.480"></a>
<FONT color="green">481</FONT>         */<a name="line.481"></a>
<FONT color="green">482</FONT>        @Override<a name="line.482"></a>
<FONT color="green">483</FONT>        protected PointValuePair optimizeInternal(int maxEval, MultivariateFunction f,<a name="line.483"></a>
<FONT color="green">484</FONT>                                                  GoalType goalType,<a name="line.484"></a>
<FONT color="green">485</FONT>                                                  OptimizationData... optData) {<a name="line.485"></a>
<FONT color="green">486</FONT>            // Scan "optData" for the input specific to this optimizer.<a name="line.486"></a>
<FONT color="green">487</FONT>            parseOptimizationData(optData);<a name="line.487"></a>
<FONT color="green">488</FONT>    <a name="line.488"></a>
<FONT color="green">489</FONT>            // The parent's method will retrieve the common parameters from<a name="line.489"></a>
<FONT color="green">490</FONT>            // "optData" and call "doOptimize".<a name="line.490"></a>
<FONT color="green">491</FONT>            return super.optimizeInternal(maxEval, f, goalType, optData);<a name="line.491"></a>
<FONT color="green">492</FONT>        }<a name="line.492"></a>
<FONT color="green">493</FONT>    <a name="line.493"></a>
<FONT color="green">494</FONT>        /** {@inheritDoc} */<a name="line.494"></a>
<FONT color="green">495</FONT>        @Override<a name="line.495"></a>
<FONT color="green">496</FONT>        protected PointValuePair doOptimize() {<a name="line.496"></a>
<FONT color="green">497</FONT>            checkParameters();<a name="line.497"></a>
<FONT color="green">498</FONT>             // -------------------- Initialization --------------------------------<a name="line.498"></a>
<FONT color="green">499</FONT>            isMinimize = getGoalType().equals(GoalType.MINIMIZE);<a name="line.499"></a>
<FONT color="green">500</FONT>            final FitnessFunction fitfun = new FitnessFunction();<a name="line.500"></a>
<FONT color="green">501</FONT>            final double[] guess = getStartPoint();<a name="line.501"></a>
<FONT color="green">502</FONT>            // number of objective variables/problem dimension<a name="line.502"></a>
<FONT color="green">503</FONT>            dimension = guess.length;<a name="line.503"></a>
<FONT color="green">504</FONT>            initializeCMA(guess);<a name="line.504"></a>
<FONT color="green">505</FONT>            iterations = 0;<a name="line.505"></a>
<FONT color="green">506</FONT>            double bestValue = fitfun.value(guess);<a name="line.506"></a>
<FONT color="green">507</FONT>            push(fitnessHistory, bestValue);<a name="line.507"></a>
<FONT color="green">508</FONT>            PointValuePair optimum = new PointValuePair(getStartPoint(),<a name="line.508"></a>
<FONT color="green">509</FONT>                    isMinimize ? bestValue : -bestValue);<a name="line.509"></a>
<FONT color="green">510</FONT>            PointValuePair lastResult = null;<a name="line.510"></a>
<FONT color="green">511</FONT>    <a name="line.511"></a>
<FONT color="green">512</FONT>            // -------------------- Generation Loop --------------------------------<a name="line.512"></a>
<FONT color="green">513</FONT>    <a name="line.513"></a>
<FONT color="green">514</FONT>            generationLoop:<a name="line.514"></a>
<FONT color="green">515</FONT>            for (iterations = 1; iterations &lt;= maxIterations; iterations++) {<a name="line.515"></a>
<FONT color="green">516</FONT>                // Generate and evaluate lambda offspring<a name="line.516"></a>
<FONT color="green">517</FONT>                final RealMatrix arz = randn1(dimension, lambda);<a name="line.517"></a>
<FONT color="green">518</FONT>                final RealMatrix arx = zeros(dimension, lambda);<a name="line.518"></a>
<FONT color="green">519</FONT>                final double[] fitness = new double[lambda];<a name="line.519"></a>
<FONT color="green">520</FONT>                // generate random offspring<a name="line.520"></a>
<FONT color="green">521</FONT>                for (int k = 0; k &lt; lambda; k++) {<a name="line.521"></a>
<FONT color="green">522</FONT>                    RealMatrix arxk = null;<a name="line.522"></a>
<FONT color="green">523</FONT>                    for (int i = 0; i &lt; checkFeasableCount + 1; i++) {<a name="line.523"></a>
<FONT color="green">524</FONT>                        if (diagonalOnly &lt;= 0) {<a name="line.524"></a>
<FONT color="green">525</FONT>                            arxk = xmean.add(BD.multiply(arz.getColumnMatrix(k))<a name="line.525"></a>
<FONT color="green">526</FONT>                                             .scalarMultiply(sigma)); // m + sig * Normal(0,C)<a name="line.526"></a>
<FONT color="green">527</FONT>                        } else {<a name="line.527"></a>
<FONT color="green">528</FONT>                            arxk = xmean.add(times(diagD,arz.getColumnMatrix(k))<a name="line.528"></a>
<FONT color="green">529</FONT>                                             .scalarMultiply(sigma));<a name="line.529"></a>
<FONT color="green">530</FONT>                        }<a name="line.530"></a>
<FONT color="green">531</FONT>                        if (i &gt;= checkFeasableCount ||<a name="line.531"></a>
<FONT color="green">532</FONT>                            fitfun.isFeasible(arxk.getColumn(0))) {<a name="line.532"></a>
<FONT color="green">533</FONT>                            break;<a name="line.533"></a>
<FONT color="green">534</FONT>                        }<a name="line.534"></a>
<FONT color="green">535</FONT>                        // regenerate random arguments for row<a name="line.535"></a>
<FONT color="green">536</FONT>                        arz.setColumn(k, randn(dimension));<a name="line.536"></a>
<FONT color="green">537</FONT>                    }<a name="line.537"></a>
<FONT color="green">538</FONT>                    copyColumn(arxk, 0, arx, k);<a name="line.538"></a>
<FONT color="green">539</FONT>                    try {<a name="line.539"></a>
<FONT color="green">540</FONT>                        fitness[k] = fitfun.value(arx.getColumn(k)); // compute fitness<a name="line.540"></a>
<FONT color="green">541</FONT>                    } catch (TooManyEvaluationsException e) {<a name="line.541"></a>
<FONT color="green">542</FONT>                        break generationLoop;<a name="line.542"></a>
<FONT color="green">543</FONT>                    }<a name="line.543"></a>
<FONT color="green">544</FONT>                }<a name="line.544"></a>
<FONT color="green">545</FONT>                // Sort by fitness and compute weighted mean into xmean<a name="line.545"></a>
<FONT color="green">546</FONT>                final int[] arindex = sortedIndices(fitness);<a name="line.546"></a>
<FONT color="green">547</FONT>                // Calculate new xmean, this is selection and recombination<a name="line.547"></a>
<FONT color="green">548</FONT>                final RealMatrix xold = xmean; // for speed up of Eq. (2) and (3)<a name="line.548"></a>
<FONT color="green">549</FONT>                final RealMatrix bestArx = selectColumns(arx, MathArrays.copyOf(arindex, mu));<a name="line.549"></a>
<FONT color="green">550</FONT>                xmean = bestArx.multiply(weights);<a name="line.550"></a>
<FONT color="green">551</FONT>                final RealMatrix bestArz = selectColumns(arz, MathArrays.copyOf(arindex, mu));<a name="line.551"></a>
<FONT color="green">552</FONT>                final RealMatrix zmean = bestArz.multiply(weights);<a name="line.552"></a>
<FONT color="green">553</FONT>                final boolean hsig = updateEvolutionPaths(zmean, xold);<a name="line.553"></a>
<FONT color="green">554</FONT>                if (diagonalOnly &lt;= 0) {<a name="line.554"></a>
<FONT color="green">555</FONT>                    updateCovariance(hsig, bestArx, arz, arindex, xold);<a name="line.555"></a>
<FONT color="green">556</FONT>                } else {<a name="line.556"></a>
<FONT color="green">557</FONT>                    updateCovarianceDiagonalOnly(hsig, bestArz);<a name="line.557"></a>
<FONT color="green">558</FONT>                }<a name="line.558"></a>
<FONT color="green">559</FONT>                // Adapt step size sigma - Eq. (5)<a name="line.559"></a>
<FONT color="green">560</FONT>                sigma *= Math.exp(Math.min(1, (normps/chiN - 1) * cs / damps));<a name="line.560"></a>
<FONT color="green">561</FONT>                final double bestFitness = fitness[arindex[0]];<a name="line.561"></a>
<FONT color="green">562</FONT>                final double worstFitness = fitness[arindex[arindex.length - 1]];<a name="line.562"></a>
<FONT color="green">563</FONT>                if (bestValue &gt; bestFitness) {<a name="line.563"></a>
<FONT color="green">564</FONT>                    bestValue = bestFitness;<a name="line.564"></a>
<FONT color="green">565</FONT>                    lastResult = optimum;<a name="line.565"></a>
<FONT color="green">566</FONT>                    optimum = new PointValuePair(fitfun.repair(bestArx.getColumn(0)),<a name="line.566"></a>
<FONT color="green">567</FONT>                                                 isMinimize ? bestFitness : -bestFitness);<a name="line.567"></a>
<FONT color="green">568</FONT>                    if (getConvergenceChecker() != null &amp;&amp;<a name="line.568"></a>
<FONT color="green">569</FONT>                        lastResult != null) {<a name="line.569"></a>
<FONT color="green">570</FONT>                        if (getConvergenceChecker().converged(iterations, optimum, lastResult)) {<a name="line.570"></a>
<FONT color="green">571</FONT>                            break generationLoop;<a name="line.571"></a>
<FONT color="green">572</FONT>                        }<a name="line.572"></a>
<FONT color="green">573</FONT>                    }<a name="line.573"></a>
<FONT color="green">574</FONT>                }<a name="line.574"></a>
<FONT color="green">575</FONT>                // handle termination criteria<a name="line.575"></a>
<FONT color="green">576</FONT>                // Break, if fitness is good enough<a name="line.576"></a>
<FONT color="green">577</FONT>                if (stopFitness != 0) { // only if stopFitness is defined<a name="line.577"></a>
<FONT color="green">578</FONT>                    if (bestFitness &lt; (isMinimize ? stopFitness : -stopFitness)) {<a name="line.578"></a>
<FONT color="green">579</FONT>                        break generationLoop;<a name="line.579"></a>
<FONT color="green">580</FONT>                    }<a name="line.580"></a>
<FONT color="green">581</FONT>                }<a name="line.581"></a>
<FONT color="green">582</FONT>                final double[] sqrtDiagC = sqrt(diagC).getColumn(0);<a name="line.582"></a>
<FONT color="green">583</FONT>                final double[] pcCol = pc.getColumn(0);<a name="line.583"></a>
<FONT color="green">584</FONT>                for (int i = 0; i &lt; dimension; i++) {<a name="line.584"></a>
<FONT color="green">585</FONT>                    if (sigma * Math.max(Math.abs(pcCol[i]), sqrtDiagC[i]) &gt; stopTolX) {<a name="line.585"></a>
<FONT color="green">586</FONT>                        break;<a name="line.586"></a>
<FONT color="green">587</FONT>                    }<a name="line.587"></a>
<FONT color="green">588</FONT>                    if (i &gt;= dimension - 1) {<a name="line.588"></a>
<FONT color="green">589</FONT>                        break generationLoop;<a name="line.589"></a>
<FONT color="green">590</FONT>                    }<a name="line.590"></a>
<FONT color="green">591</FONT>                }<a name="line.591"></a>
<FONT color="green">592</FONT>                for (int i = 0; i &lt; dimension; i++) {<a name="line.592"></a>
<FONT color="green">593</FONT>                    if (sigma * sqrtDiagC[i] &gt; stopTolUpX) {<a name="line.593"></a>
<FONT color="green">594</FONT>                        break generationLoop;<a name="line.594"></a>
<FONT color="green">595</FONT>                    }<a name="line.595"></a>
<FONT color="green">596</FONT>                }<a name="line.596"></a>
<FONT color="green">597</FONT>                final double historyBest = min(fitnessHistory);<a name="line.597"></a>
<FONT color="green">598</FONT>                final double historyWorst = max(fitnessHistory);<a name="line.598"></a>
<FONT color="green">599</FONT>                if (iterations &gt; 2 &amp;&amp;<a name="line.599"></a>
<FONT color="green">600</FONT>                    Math.max(historyWorst, worstFitness) -<a name="line.600"></a>
<FONT color="green">601</FONT>                    Math.min(historyBest, bestFitness) &lt; stopTolFun) {<a name="line.601"></a>
<FONT color="green">602</FONT>                    break generationLoop;<a name="line.602"></a>
<FONT color="green">603</FONT>                }<a name="line.603"></a>
<FONT color="green">604</FONT>                if (iterations &gt; fitnessHistory.length &amp;&amp;<a name="line.604"></a>
<FONT color="green">605</FONT>                    historyWorst-historyBest &lt; stopTolHistFun) {<a name="line.605"></a>
<FONT color="green">606</FONT>                    break generationLoop;<a name="line.606"></a>
<FONT color="green">607</FONT>                }<a name="line.607"></a>
<FONT color="green">608</FONT>                // condition number of the covariance matrix exceeds 1e14<a name="line.608"></a>
<FONT color="green">609</FONT>                if (max(diagD)/min(diagD) &gt; 1e7) {<a name="line.609"></a>
<FONT color="green">610</FONT>                    break generationLoop;<a name="line.610"></a>
<FONT color="green">611</FONT>                }<a name="line.611"></a>
<FONT color="green">612</FONT>                // user defined termination<a name="line.612"></a>
<FONT color="green">613</FONT>                if (getConvergenceChecker() != null) {<a name="line.613"></a>
<FONT color="green">614</FONT>                    final PointValuePair current<a name="line.614"></a>
<FONT color="green">615</FONT>                        = new PointValuePair(bestArx.getColumn(0),<a name="line.615"></a>
<FONT color="green">616</FONT>                                             isMinimize ? bestFitness : -bestFitness);<a name="line.616"></a>
<FONT color="green">617</FONT>                    if (lastResult != null &amp;&amp;<a name="line.617"></a>
<FONT color="green">618</FONT>                        getConvergenceChecker().converged(iterations, current, lastResult)) {<a name="line.618"></a>
<FONT color="green">619</FONT>                        break generationLoop;<a name="line.619"></a>
<FONT color="green">620</FONT>                        }<a name="line.620"></a>
<FONT color="green">621</FONT>                    lastResult = current;<a name="line.621"></a>
<FONT color="green">622</FONT>                }<a name="line.622"></a>
<FONT color="green">623</FONT>                // Adjust step size in case of equal function values (flat fitness)<a name="line.623"></a>
<FONT color="green">624</FONT>                if (bestValue == fitness[arindex[(int)(0.1+lambda/4.)]]) {<a name="line.624"></a>
<FONT color="green">625</FONT>                    sigma = sigma * Math.exp(0.2 + cs / damps);<a name="line.625"></a>
<FONT color="green">626</FONT>                }<a name="line.626"></a>
<FONT color="green">627</FONT>                if (iterations &gt; 2 &amp;&amp; Math.max(historyWorst, bestFitness) -<a name="line.627"></a>
<FONT color="green">628</FONT>                    Math.min(historyBest, bestFitness) == 0) {<a name="line.628"></a>
<FONT color="green">629</FONT>                    sigma = sigma * Math.exp(0.2 + cs / damps);<a name="line.629"></a>
<FONT color="green">630</FONT>                }<a name="line.630"></a>
<FONT color="green">631</FONT>                // store best in history<a name="line.631"></a>
<FONT color="green">632</FONT>                push(fitnessHistory,bestFitness);<a name="line.632"></a>
<FONT color="green">633</FONT>                fitfun.setValueRange(worstFitness-bestFitness);<a name="line.633"></a>
<FONT color="green">634</FONT>                if (generateStatistics) {<a name="line.634"></a>
<FONT color="green">635</FONT>                    statisticsSigmaHistory.add(sigma);<a name="line.635"></a>
<FONT color="green">636</FONT>                    statisticsFitnessHistory.add(bestFitness);<a name="line.636"></a>
<FONT color="green">637</FONT>                    statisticsMeanHistory.add(xmean.transpose());<a name="line.637"></a>
<FONT color="green">638</FONT>                    statisticsDHistory.add(diagD.transpose().scalarMultiply(1E5));<a name="line.638"></a>
<FONT color="green">639</FONT>                }<a name="line.639"></a>
<FONT color="green">640</FONT>            }<a name="line.640"></a>
<FONT color="green">641</FONT>            return optimum;<a name="line.641"></a>
<FONT color="green">642</FONT>        }<a name="line.642"></a>
<FONT color="green">643</FONT>    <a name="line.643"></a>
<FONT color="green">644</FONT>        /**<a name="line.644"></a>
<FONT color="green">645</FONT>         * Scans the list of (required and optional) optimization data that<a name="line.645"></a>
<FONT color="green">646</FONT>         * characterize the problem.<a name="line.646"></a>
<FONT color="green">647</FONT>         *<a name="line.647"></a>
<FONT color="green">648</FONT>         * @param optData Optimization data. The following data will be looked for:<a name="line.648"></a>
<FONT color="green">649</FONT>         * &lt;ul&gt;<a name="line.649"></a>
<FONT color="green">650</FONT>         *  &lt;li&gt;{@link Sigma}&lt;/li&gt;<a name="line.650"></a>
<FONT color="green">651</FONT>         *  &lt;li&gt;{@link PopulationSize}&lt;/li&gt;<a name="line.651"></a>
<FONT color="green">652</FONT>         * &lt;/ul&gt;<a name="line.652"></a>
<FONT color="green">653</FONT>         */<a name="line.653"></a>
<FONT color="green">654</FONT>        private void parseOptimizationData(OptimizationData... optData) {<a name="line.654"></a>
<FONT color="green">655</FONT>            // The existing values (as set by the previous call) are reused if<a name="line.655"></a>
<FONT color="green">656</FONT>            // not provided in the argument list.<a name="line.656"></a>
<FONT color="green">657</FONT>            for (OptimizationData data : optData) {<a name="line.657"></a>
<FONT color="green">658</FONT>                if (data instanceof Sigma) {<a name="line.658"></a>
<FONT color="green">659</FONT>                    inputSigma = ((Sigma) data).getSigma();<a name="line.659"></a>
<FONT color="green">660</FONT>                    continue;<a name="line.660"></a>
<FONT color="green">661</FONT>                }<a name="line.661"></a>
<FONT color="green">662</FONT>                if (data instanceof PopulationSize) {<a name="line.662"></a>
<FONT color="green">663</FONT>                    lambda = ((PopulationSize) data).getPopulationSize();<a name="line.663"></a>
<FONT color="green">664</FONT>                    continue;<a name="line.664"></a>
<FONT color="green">665</FONT>                }<a name="line.665"></a>
<FONT color="green">666</FONT>            }<a name="line.666"></a>
<FONT color="green">667</FONT>        }<a name="line.667"></a>
<FONT color="green">668</FONT>    <a name="line.668"></a>
<FONT color="green">669</FONT>        /**<a name="line.669"></a>
<FONT color="green">670</FONT>         * Checks dimensions and values of boundaries and inputSigma if defined.<a name="line.670"></a>
<FONT color="green">671</FONT>         */<a name="line.671"></a>
<FONT color="green">672</FONT>        private void checkParameters() {<a name="line.672"></a>
<FONT color="green">673</FONT>            final double[] init = getStartPoint();<a name="line.673"></a>
<FONT color="green">674</FONT>            final double[] lB = getLowerBound();<a name="line.674"></a>
<FONT color="green">675</FONT>            final double[] uB = getUpperBound();<a name="line.675"></a>
<FONT color="green">676</FONT>    <a name="line.676"></a>
<FONT color="green">677</FONT>            if (inputSigma != null) {<a name="line.677"></a>
<FONT color="green">678</FONT>                if (inputSigma.length != init.length) {<a name="line.678"></a>
<FONT color="green">679</FONT>                    throw new DimensionMismatchException(inputSigma.length, init.length);<a name="line.679"></a>
<FONT color="green">680</FONT>                }<a name="line.680"></a>
<FONT color="green">681</FONT>                for (int i = 0; i &lt; init.length; i++) {<a name="line.681"></a>
<FONT color="green">682</FONT>                    if (inputSigma[i] &lt; 0) {<a name="line.682"></a>
<FONT color="green">683</FONT>                        // XXX Remove this block in 4.0 (check performed in "Sigma" class).<a name="line.683"></a>
<FONT color="green">684</FONT>                        throw new NotPositiveException(inputSigma[i]);<a name="line.684"></a>
<FONT color="green">685</FONT>                    }<a name="line.685"></a>
<FONT color="green">686</FONT>                    if (inputSigma[i] &gt; uB[i] - lB[i]) {<a name="line.686"></a>
<FONT color="green">687</FONT>                        throw new OutOfRangeException(inputSigma[i], 0, uB[i] - lB[i]);<a name="line.687"></a>
<FONT color="green">688</FONT>                    }<a name="line.688"></a>
<FONT color="green">689</FONT>                }<a name="line.689"></a>
<FONT color="green">690</FONT>            }<a name="line.690"></a>
<FONT color="green">691</FONT>        }<a name="line.691"></a>
<FONT color="green">692</FONT>    <a name="line.692"></a>
<FONT color="green">693</FONT>        /**<a name="line.693"></a>
<FONT color="green">694</FONT>         * Initialization of the dynamic search parameters<a name="line.694"></a>
<FONT color="green">695</FONT>         *<a name="line.695"></a>
<FONT color="green">696</FONT>         * @param guess Initial guess for the arguments of the fitness function.<a name="line.696"></a>
<FONT color="green">697</FONT>         */<a name="line.697"></a>
<FONT color="green">698</FONT>        private void initializeCMA(double[] guess) {<a name="line.698"></a>
<FONT color="green">699</FONT>            if (lambda &lt;= 0) {<a name="line.699"></a>
<FONT color="green">700</FONT>                // XXX Line below to replace the current one in 4.0 (MATH-879).<a name="line.700"></a>
<FONT color="green">701</FONT>                // throw new NotStrictlyPositiveException(lambda);<a name="line.701"></a>
<FONT color="green">702</FONT>                lambda = 4 + (int) (3 * Math.log(dimension));<a name="line.702"></a>
<FONT color="green">703</FONT>            }<a name="line.703"></a>
<FONT color="green">704</FONT>            // initialize sigma<a name="line.704"></a>
<FONT color="green">705</FONT>            final double[][] sigmaArray = new double[guess.length][1];<a name="line.705"></a>
<FONT color="green">706</FONT>            for (int i = 0; i &lt; guess.length; i++) {<a name="line.706"></a>
<FONT color="green">707</FONT>                // XXX Line below to replace the current one in 4.0 (MATH-868).<a name="line.707"></a>
<FONT color="green">708</FONT>                // sigmaArray[i][0] = inputSigma[i];<a name="line.708"></a>
<FONT color="green">709</FONT>                sigmaArray[i][0] = inputSigma == null ? 0.3 : inputSigma[i];<a name="line.709"></a>
<FONT color="green">710</FONT>            }<a name="line.710"></a>
<FONT color="green">711</FONT>            final RealMatrix insigma = new Array2DRowRealMatrix(sigmaArray, false);<a name="line.711"></a>
<FONT color="green">712</FONT>            sigma = max(insigma); // overall standard deviation<a name="line.712"></a>
<FONT color="green">713</FONT>    <a name="line.713"></a>
<FONT color="green">714</FONT>            // initialize termination criteria<a name="line.714"></a>
<FONT color="green">715</FONT>            stopTolUpX = 1e3 * max(insigma);<a name="line.715"></a>
<FONT color="green">716</FONT>            stopTolX = 1e-11 * max(insigma);<a name="line.716"></a>
<FONT color="green">717</FONT>            stopTolFun = 1e-12;<a name="line.717"></a>
<FONT color="green">718</FONT>            stopTolHistFun = 1e-13;<a name="line.718"></a>
<FONT color="green">719</FONT>    <a name="line.719"></a>
<FONT color="green">720</FONT>            // initialize selection strategy parameters<a name="line.720"></a>
<FONT color="green">721</FONT>            mu = lambda / 2; // number of parents/points for recombination<a name="line.721"></a>
<FONT color="green">722</FONT>            logMu2 = Math.log(mu + 0.5);<a name="line.722"></a>
<FONT color="green">723</FONT>            weights = log(sequence(1, mu, 1)).scalarMultiply(-1).scalarAdd(logMu2);<a name="line.723"></a>
<FONT color="green">724</FONT>            double sumw = 0;<a name="line.724"></a>
<FONT color="green">725</FONT>            double sumwq = 0;<a name="line.725"></a>
<FONT color="green">726</FONT>            for (int i = 0; i &lt; mu; i++) {<a name="line.726"></a>
<FONT color="green">727</FONT>                double w = weights.getEntry(i, 0);<a name="line.727"></a>
<FONT color="green">728</FONT>                sumw += w;<a name="line.728"></a>
<FONT color="green">729</FONT>                sumwq += w * w;<a name="line.729"></a>
<FONT color="green">730</FONT>            }<a name="line.730"></a>
<FONT color="green">731</FONT>            weights = weights.scalarMultiply(1 / sumw);<a name="line.731"></a>
<FONT color="green">732</FONT>            mueff = sumw * sumw / sumwq; // variance-effectiveness of sum w_i x_i<a name="line.732"></a>
<FONT color="green">733</FONT>    <a name="line.733"></a>
<FONT color="green">734</FONT>            // initialize dynamic strategy parameters and constants<a name="line.734"></a>
<FONT color="green">735</FONT>            cc = (4 + mueff / dimension) /<a name="line.735"></a>
<FONT color="green">736</FONT>                    (dimension + 4 + 2 * mueff / dimension);<a name="line.736"></a>
<FONT color="green">737</FONT>            cs = (mueff + 2) / (dimension + mueff + 3.);<a name="line.737"></a>
<FONT color="green">738</FONT>            damps = (1 + 2 * Math.max(0, Math.sqrt((mueff - 1) /<a name="line.738"></a>
<FONT color="green">739</FONT>                                                   (dimension + 1)) - 1)) *<a name="line.739"></a>
<FONT color="green">740</FONT>                Math.max(0.3,<a name="line.740"></a>
<FONT color="green">741</FONT>                         1 - dimension / (1e-6 + maxIterations)) + cs; // minor increment<a name="line.741"></a>
<FONT color="green">742</FONT>            ccov1 = 2 / ((dimension + 1.3) * (dimension + 1.3) + mueff);<a name="line.742"></a>
<FONT color="green">743</FONT>            ccovmu = Math.min(1 - ccov1, 2 * (mueff - 2 + 1 / mueff) /<a name="line.743"></a>
<FONT color="green">744</FONT>                              ((dimension + 2) * (dimension + 2) + mueff));<a name="line.744"></a>
<FONT color="green">745</FONT>            ccov1Sep = Math.min(1, ccov1 * (dimension + 1.5) / 3);<a name="line.745"></a>
<FONT color="green">746</FONT>            ccovmuSep = Math.min(1 - ccov1, ccovmu * (dimension + 1.5) / 3);<a name="line.746"></a>
<FONT color="green">747</FONT>            chiN = Math.sqrt(dimension) *<a name="line.747"></a>
<FONT color="green">748</FONT>                (1 - 1 / ((double) 4 * dimension) + 1 / ((double) 21 * dimension * dimension));<a name="line.748"></a>
<FONT color="green">749</FONT>            // intialize CMA internal values - updated each generation<a name="line.749"></a>
<FONT color="green">750</FONT>            xmean = MatrixUtils.createColumnRealMatrix(guess); // objective variables<a name="line.750"></a>
<FONT color="green">751</FONT>            diagD = insigma.scalarMultiply(1 / sigma);<a name="line.751"></a>
<FONT color="green">752</FONT>            diagC = square(diagD);<a name="line.752"></a>
<FONT color="green">753</FONT>            pc = zeros(dimension, 1); // evolution paths for C and sigma<a name="line.753"></a>
<FONT color="green">754</FONT>            ps = zeros(dimension, 1); // B defines the coordinate system<a name="line.754"></a>
<FONT color="green">755</FONT>            normps = ps.getFrobeniusNorm();<a name="line.755"></a>
<FONT color="green">756</FONT>    <a name="line.756"></a>
<FONT color="green">757</FONT>            B = eye(dimension, dimension);<a name="line.757"></a>
<FONT color="green">758</FONT>            D = ones(dimension, 1); // diagonal D defines the scaling<a name="line.758"></a>
<FONT color="green">759</FONT>            BD = times(B, repmat(diagD.transpose(), dimension, 1));<a name="line.759"></a>
<FONT color="green">760</FONT>            C = B.multiply(diag(square(D)).multiply(B.transpose())); // covariance<a name="line.760"></a>
<FONT color="green">761</FONT>            historySize = 10 + (int) (3 * 10 * dimension / (double) lambda);<a name="line.761"></a>
<FONT color="green">762</FONT>            fitnessHistory = new double[historySize]; // history of fitness values<a name="line.762"></a>
<FONT color="green">763</FONT>            for (int i = 0; i &lt; historySize; i++) {<a name="line.763"></a>
<FONT color="green">764</FONT>                fitnessHistory[i] = Double.MAX_VALUE;<a name="line.764"></a>
<FONT color="green">765</FONT>            }<a name="line.765"></a>
<FONT color="green">766</FONT>        }<a name="line.766"></a>
<FONT color="green">767</FONT>    <a name="line.767"></a>
<FONT color="green">768</FONT>        /**<a name="line.768"></a>
<FONT color="green">769</FONT>         * Update of the evolution paths ps and pc.<a name="line.769"></a>
<FONT color="green">770</FONT>         *<a name="line.770"></a>
<FONT color="green">771</FONT>         * @param zmean Weighted row matrix of the gaussian random numbers generating<a name="line.771"></a>
<FONT color="green">772</FONT>         * the current offspring.<a name="line.772"></a>
<FONT color="green">773</FONT>         * @param xold xmean matrix of the previous generation.<a name="line.773"></a>
<FONT color="green">774</FONT>         * @return hsig flag indicating a small correction.<a name="line.774"></a>
<FONT color="green">775</FONT>         */<a name="line.775"></a>
<FONT color="green">776</FONT>        private boolean updateEvolutionPaths(RealMatrix zmean, RealMatrix xold) {<a name="line.776"></a>
<FONT color="green">777</FONT>            ps = ps.scalarMultiply(1 - cs).add(<a name="line.777"></a>
<FONT color="green">778</FONT>                    B.multiply(zmean).scalarMultiply(<a name="line.778"></a>
<FONT color="green">779</FONT>                            Math.sqrt(cs * (2 - cs) * mueff)));<a name="line.779"></a>
<FONT color="green">780</FONT>            normps = ps.getFrobeniusNorm();<a name="line.780"></a>
<FONT color="green">781</FONT>            final boolean hsig = normps /<a name="line.781"></a>
<FONT color="green">782</FONT>                Math.sqrt(1 - Math.pow(1 - cs, 2 * iterations)) /<a name="line.782"></a>
<FONT color="green">783</FONT>                chiN &lt; 1.4 + 2 / ((double) dimension + 1);<a name="line.783"></a>
<FONT color="green">784</FONT>            pc = pc.scalarMultiply(1 - cc);<a name="line.784"></a>
<FONT color="green">785</FONT>            if (hsig) {<a name="line.785"></a>
<FONT color="green">786</FONT>                pc = pc.add(xmean.subtract(xold).scalarMultiply(Math.sqrt(cc * (2 - cc) * mueff) / sigma));<a name="line.786"></a>
<FONT color="green">787</FONT>            }<a name="line.787"></a>
<FONT color="green">788</FONT>            return hsig;<a name="line.788"></a>
<FONT color="green">789</FONT>        }<a name="line.789"></a>
<FONT color="green">790</FONT>    <a name="line.790"></a>
<FONT color="green">791</FONT>        /**<a name="line.791"></a>
<FONT color="green">792</FONT>         * Update of the covariance matrix C for diagonalOnly &gt; 0<a name="line.792"></a>
<FONT color="green">793</FONT>         *<a name="line.793"></a>
<FONT color="green">794</FONT>         * @param hsig Flag indicating a small correction.<a name="line.794"></a>
<FONT color="green">795</FONT>         * @param bestArz Fitness-sorted matrix of the gaussian random values of the<a name="line.795"></a>
<FONT color="green">796</FONT>         * current offspring.<a name="line.796"></a>
<FONT color="green">797</FONT>         */<a name="line.797"></a>
<FONT color="green">798</FONT>        private void updateCovarianceDiagonalOnly(boolean hsig,<a name="line.798"></a>
<FONT color="green">799</FONT>                                                  final RealMatrix bestArz) {<a name="line.799"></a>
<FONT color="green">800</FONT>            // minor correction if hsig==false<a name="line.800"></a>
<FONT color="green">801</FONT>            double oldFac = hsig ? 0 : ccov1Sep * cc * (2 - cc);<a name="line.801"></a>
<FONT color="green">802</FONT>            oldFac += 1 - ccov1Sep - ccovmuSep;<a name="line.802"></a>
<FONT color="green">803</FONT>            diagC = diagC.scalarMultiply(oldFac) // regard old matrix<a name="line.803"></a>
<FONT color="green">804</FONT>                .add(square(pc).scalarMultiply(ccov1Sep)) // plus rank one update<a name="line.804"></a>
<FONT color="green">805</FONT>                .add((times(diagC, square(bestArz).multiply(weights))) // plus rank mu update<a name="line.805"></a>
<FONT color="green">806</FONT>                     .scalarMultiply(ccovmuSep));<a name="line.806"></a>
<FONT color="green">807</FONT>            diagD = sqrt(diagC); // replaces eig(C)<a name="line.807"></a>
<FONT color="green">808</FONT>            if (diagonalOnly &gt; 1 &amp;&amp;<a name="line.808"></a>
<FONT color="green">809</FONT>                iterations &gt; diagonalOnly) {<a name="line.809"></a>
<FONT color="green">810</FONT>                // full covariance matrix from now on<a name="line.810"></a>
<FONT color="green">811</FONT>                diagonalOnly = 0;<a name="line.811"></a>
<FONT color="green">812</FONT>                B = eye(dimension, dimension);<a name="line.812"></a>
<FONT color="green">813</FONT>                BD = diag(diagD);<a name="line.813"></a>
<FONT color="green">814</FONT>                C = diag(diagC);<a name="line.814"></a>
<FONT color="green">815</FONT>            }<a name="line.815"></a>
<FONT color="green">816</FONT>        }<a name="line.816"></a>
<FONT color="green">817</FONT>    <a name="line.817"></a>
<FONT color="green">818</FONT>        /**<a name="line.818"></a>
<FONT color="green">819</FONT>         * Update of the covariance matrix C.<a name="line.819"></a>
<FONT color="green">820</FONT>         *<a name="line.820"></a>
<FONT color="green">821</FONT>         * @param hsig Flag indicating a small correction.<a name="line.821"></a>
<FONT color="green">822</FONT>         * @param bestArx Fitness-sorted matrix of the argument vectors producing the<a name="line.822"></a>
<FONT color="green">823</FONT>         * current offspring.<a name="line.823"></a>
<FONT color="green">824</FONT>         * @param arz Unsorted matrix containing the gaussian random values of the<a name="line.824"></a>
<FONT color="green">825</FONT>         * current offspring.<a name="line.825"></a>
<FONT color="green">826</FONT>         * @param arindex Indices indicating the fitness-order of the current offspring.<a name="line.826"></a>
<FONT color="green">827</FONT>         * @param xold xmean matrix of the previous generation.<a name="line.827"></a>
<FONT color="green">828</FONT>         */<a name="line.828"></a>
<FONT color="green">829</FONT>        private void updateCovariance(boolean hsig, final RealMatrix bestArx,<a name="line.829"></a>
<FONT color="green">830</FONT>                                      final RealMatrix arz, final int[] arindex,<a name="line.830"></a>
<FONT color="green">831</FONT>                                      final RealMatrix xold) {<a name="line.831"></a>
<FONT color="green">832</FONT>            double negccov = 0;<a name="line.832"></a>
<FONT color="green">833</FONT>            if (ccov1 + ccovmu &gt; 0) {<a name="line.833"></a>
<FONT color="green">834</FONT>                final RealMatrix arpos = bestArx.subtract(repmat(xold, 1, mu))<a name="line.834"></a>
<FONT color="green">835</FONT>                    .scalarMultiply(1 / sigma); // mu difference vectors<a name="line.835"></a>
<FONT color="green">836</FONT>                final RealMatrix roneu = pc.multiply(pc.transpose())<a name="line.836"></a>
<FONT color="green">837</FONT>                    .scalarMultiply(ccov1); // rank one update<a name="line.837"></a>
<FONT color="green">838</FONT>                // minor correction if hsig==false<a name="line.838"></a>
<FONT color="green">839</FONT>                double oldFac = hsig ? 0 : ccov1 * cc * (2 - cc);<a name="line.839"></a>
<FONT color="green">840</FONT>                oldFac += 1 - ccov1 - ccovmu;<a name="line.840"></a>
<FONT color="green">841</FONT>                if (isActiveCMA) {<a name="line.841"></a>
<FONT color="green">842</FONT>                    // Adapt covariance matrix C active CMA<a name="line.842"></a>
<FONT color="green">843</FONT>                    negccov = (1 - ccovmu) * 0.25 * mueff /<a name="line.843"></a>
<FONT color="green">844</FONT>                        (Math.pow(dimension + 2, 1.5) + 2 * mueff);<a name="line.844"></a>
<FONT color="green">845</FONT>                    // keep at least 0.66 in all directions, small popsize are most<a name="line.845"></a>
<FONT color="green">846</FONT>                    // critical<a name="line.846"></a>
<FONT color="green">847</FONT>                    final double negminresidualvariance = 0.66;<a name="line.847"></a>
<FONT color="green">848</FONT>                    // where to make up for the variance loss<a name="line.848"></a>
<FONT color="green">849</FONT>                    final double negalphaold = 0.5;<a name="line.849"></a>
<FONT color="green">850</FONT>                    // prepare vectors, compute negative updating matrix Cneg<a name="line.850"></a>
<FONT color="green">851</FONT>                    final int[] arReverseIndex = reverse(arindex);<a name="line.851"></a>
<FONT color="green">852</FONT>                    RealMatrix arzneg = selectColumns(arz, MathArrays.copyOf(arReverseIndex, mu));<a name="line.852"></a>
<FONT color="green">853</FONT>                    RealMatrix arnorms = sqrt(sumRows(square(arzneg)));<a name="line.853"></a>
<FONT color="green">854</FONT>                    final int[] idxnorms = sortedIndices(arnorms.getRow(0));<a name="line.854"></a>
<FONT color="green">855</FONT>                    final RealMatrix arnormsSorted = selectColumns(arnorms, idxnorms);<a name="line.855"></a>
<FONT color="green">856</FONT>                    final int[] idxReverse = reverse(idxnorms);<a name="line.856"></a>
<FONT color="green">857</FONT>                    final RealMatrix arnormsReverse = selectColumns(arnorms, idxReverse);<a name="line.857"></a>
<FONT color="green">858</FONT>                    arnorms = divide(arnormsReverse, arnormsSorted);<a name="line.858"></a>
<FONT color="green">859</FONT>                    final int[] idxInv = inverse(idxnorms);<a name="line.859"></a>
<FONT color="green">860</FONT>                    final RealMatrix arnormsInv = selectColumns(arnorms, idxInv);<a name="line.860"></a>
<FONT color="green">861</FONT>                    // check and set learning rate negccov<a name="line.861"></a>
<FONT color="green">862</FONT>                    final double negcovMax = (1 - negminresidualvariance) /<a name="line.862"></a>
<FONT color="green">863</FONT>                        square(arnormsInv).multiply(weights).getEntry(0, 0);<a name="line.863"></a>
<FONT color="green">864</FONT>                    if (negccov &gt; negcovMax) {<a name="line.864"></a>
<FONT color="green">865</FONT>                        negccov = negcovMax;<a name="line.865"></a>
<FONT color="green">866</FONT>                    }<a name="line.866"></a>
<FONT color="green">867</FONT>                    arzneg = times(arzneg, repmat(arnormsInv, dimension, 1));<a name="line.867"></a>
<FONT color="green">868</FONT>                    final RealMatrix artmp = BD.multiply(arzneg);<a name="line.868"></a>
<FONT color="green">869</FONT>                    final RealMatrix Cneg = artmp.multiply(diag(weights)).multiply(artmp.transpose());<a name="line.869"></a>
<FONT color="green">870</FONT>                    oldFac += negalphaold * negccov;<a name="line.870"></a>
<FONT color="green">871</FONT>                    C = C.scalarMultiply(oldFac)<a name="line.871"></a>
<FONT color="green">872</FONT>                        .add(roneu) // regard old matrix<a name="line.872"></a>
<FONT color="green">873</FONT>                        .add(arpos.scalarMultiply( // plus rank one update<a name="line.873"></a>
<FONT color="green">874</FONT>                                                  ccovmu + (1 - negalphaold) * negccov) // plus rank mu update<a name="line.874"></a>
<FONT color="green">875</FONT>                             .multiply(times(repmat(weights, 1, dimension),<a name="line.875"></a>
<FONT color="green">876</FONT>                                             arpos.transpose())))<a name="line.876"></a>
<FONT color="green">877</FONT>                        .subtract(Cneg.scalarMultiply(negccov));<a name="line.877"></a>
<FONT color="green">878</FONT>                } else {<a name="line.878"></a>
<FONT color="green">879</FONT>                    // Adapt covariance matrix C - nonactive<a name="line.879"></a>
<FONT color="green">880</FONT>                    C = C.scalarMultiply(oldFac) // regard old matrix<a name="line.880"></a>
<FONT color="green">881</FONT>                        .add(roneu) // plus rank one update<a name="line.881"></a>
<FONT color="green">882</FONT>                        .add(arpos.scalarMultiply(ccovmu) // plus rank mu update<a name="line.882"></a>
<FONT color="green">883</FONT>                             .multiply(times(repmat(weights, 1, dimension),<a name="line.883"></a>
<FONT color="green">884</FONT>                                             arpos.transpose())));<a name="line.884"></a>
<FONT color="green">885</FONT>                }<a name="line.885"></a>
<FONT color="green">886</FONT>            }<a name="line.886"></a>
<FONT color="green">887</FONT>            updateBD(negccov);<a name="line.887"></a>
<FONT color="green">888</FONT>        }<a name="line.888"></a>
<FONT color="green">889</FONT>    <a name="line.889"></a>
<FONT color="green">890</FONT>        /**<a name="line.890"></a>
<FONT color="green">891</FONT>         * Update B and D from C.<a name="line.891"></a>
<FONT color="green">892</FONT>         *<a name="line.892"></a>
<FONT color="green">893</FONT>         * @param negccov Negative covariance factor.<a name="line.893"></a>
<FONT color="green">894</FONT>         */<a name="line.894"></a>
<FONT color="green">895</FONT>        private void updateBD(double negccov) {<a name="line.895"></a>
<FONT color="green">896</FONT>            if (ccov1 + ccovmu + negccov &gt; 0 &amp;&amp;<a name="line.896"></a>
<FONT color="green">897</FONT>                (iterations % 1. / (ccov1 + ccovmu + negccov) / dimension / 10.) &lt; 1) {<a name="line.897"></a>
<FONT color="green">898</FONT>                // to achieve O(N^2)<a name="line.898"></a>
<FONT color="green">899</FONT>                C = triu(C, 0).add(triu(C, 1).transpose());<a name="line.899"></a>
<FONT color="green">900</FONT>                // enforce symmetry to prevent complex numbers<a name="line.900"></a>
<FONT color="green">901</FONT>                final EigenDecomposition eig = new EigenDecomposition(C);<a name="line.901"></a>
<FONT color="green">902</FONT>                B = eig.getV(); // eigen decomposition, B==normalized eigenvectors<a name="line.902"></a>
<FONT color="green">903</FONT>                D = eig.getD();<a name="line.903"></a>
<FONT color="green">904</FONT>                diagD = diag(D);<a name="line.904"></a>
<FONT color="green">905</FONT>                if (min(diagD) &lt;= 0) {<a name="line.905"></a>
<FONT color="green">906</FONT>                    for (int i = 0; i &lt; dimension; i++) {<a name="line.906"></a>
<FONT color="green">907</FONT>                        if (diagD.getEntry(i, 0) &lt; 0) {<a name="line.907"></a>
<FONT color="green">908</FONT>                            diagD.setEntry(i, 0, 0);<a name="line.908"></a>
<FONT color="green">909</FONT>                        }<a name="line.909"></a>
<FONT color="green">910</FONT>                    }<a name="line.910"></a>
<FONT color="green">911</FONT>                    final double tfac = max(diagD) / 1e14;<a name="line.911"></a>
<FONT color="green">912</FONT>                    C = C.add(eye(dimension, dimension).scalarMultiply(tfac));<a name="line.912"></a>
<FONT color="green">913</FONT>                    diagD = diagD.add(ones(dimension, 1).scalarMultiply(tfac));<a name="line.913"></a>
<FONT color="green">914</FONT>                }<a name="line.914"></a>
<FONT color="green">915</FONT>                if (max(diagD) &gt; 1e14 * min(diagD)) {<a name="line.915"></a>
<FONT color="green">916</FONT>                    final double tfac = max(diagD) / 1e14 - min(diagD);<a name="line.916"></a>
<FONT color="green">917</FONT>                    C = C.add(eye(dimension, dimension).scalarMultiply(tfac));<a name="line.917"></a>
<FONT color="green">918</FONT>                    diagD = diagD.add(ones(dimension, 1).scalarMultiply(tfac));<a name="line.918"></a>
<FONT color="green">919</FONT>                }<a name="line.919"></a>
<FONT color="green">920</FONT>                diagC = diag(C);<a name="line.920"></a>
<FONT color="green">921</FONT>                diagD = sqrt(diagD); // D contains standard deviations now<a name="line.921"></a>
<FONT color="green">922</FONT>                BD = times(B, repmat(diagD.transpose(), dimension, 1)); // O(n^2)<a name="line.922"></a>
<FONT color="green">923</FONT>            }<a name="line.923"></a>
<FONT color="green">924</FONT>        }<a name="line.924"></a>
<FONT color="green">925</FONT>    <a name="line.925"></a>
<FONT color="green">926</FONT>        /**<a name="line.926"></a>
<FONT color="green">927</FONT>         * Pushes the current best fitness value in a history queue.<a name="line.927"></a>
<FONT color="green">928</FONT>         *<a name="line.928"></a>
<FONT color="green">929</FONT>         * @param vals History queue.<a name="line.929"></a>
<FONT color="green">930</FONT>         * @param val Current best fitness value.<a name="line.930"></a>
<FONT color="green">931</FONT>         */<a name="line.931"></a>
<FONT color="green">932</FONT>        private static void push(double[] vals, double val) {<a name="line.932"></a>
<FONT color="green">933</FONT>            for (int i = vals.length-1; i &gt; 0; i--) {<a name="line.933"></a>
<FONT color="green">934</FONT>                vals[i] = vals[i-1];<a name="line.934"></a>
<FONT color="green">935</FONT>            }<a name="line.935"></a>
<FONT color="green">936</FONT>            vals[0] = val;<a name="line.936"></a>
<FONT color="green">937</FONT>        }<a name="line.937"></a>
<FONT color="green">938</FONT>    <a name="line.938"></a>
<FONT color="green">939</FONT>        /**<a name="line.939"></a>
<FONT color="green">940</FONT>         * Sorts fitness values.<a name="line.940"></a>
<FONT color="green">941</FONT>         *<a name="line.941"></a>
<FONT color="green">942</FONT>         * @param doubles Array of values to be sorted.<a name="line.942"></a>
<FONT color="green">943</FONT>         * @return a sorted array of indices pointing into doubles.<a name="line.943"></a>
<FONT color="green">944</FONT>         */<a name="line.944"></a>
<FONT color="green">945</FONT>        private int[] sortedIndices(final double[] doubles) {<a name="line.945"></a>
<FONT color="green">946</FONT>            final DoubleIndex[] dis = new DoubleIndex[doubles.length];<a name="line.946"></a>
<FONT color="green">947</FONT>            for (int i = 0; i &lt; doubles.length; i++) {<a name="line.947"></a>
<FONT color="green">948</FONT>                dis[i] = new DoubleIndex(doubles[i], i);<a name="line.948"></a>
<FONT color="green">949</FONT>            }<a name="line.949"></a>
<FONT color="green">950</FONT>            Arrays.sort(dis);<a name="line.950"></a>
<FONT color="green">951</FONT>            final int[] indices = new int[doubles.length];<a name="line.951"></a>
<FONT color="green">952</FONT>            for (int i = 0; i &lt; doubles.length; i++) {<a name="line.952"></a>
<FONT color="green">953</FONT>                indices[i] = dis[i].index;<a name="line.953"></a>
<FONT color="green">954</FONT>            }<a name="line.954"></a>
<FONT color="green">955</FONT>            return indices;<a name="line.955"></a>
<FONT color="green">956</FONT>        }<a name="line.956"></a>
<FONT color="green">957</FONT>    <a name="line.957"></a>
<FONT color="green">958</FONT>        /**<a name="line.958"></a>
<FONT color="green">959</FONT>         * Used to sort fitness values. Sorting is always in lower value first<a name="line.959"></a>
<FONT color="green">960</FONT>         * order.<a name="line.960"></a>
<FONT color="green">961</FONT>         */<a name="line.961"></a>
<FONT color="green">962</FONT>        private static class DoubleIndex implements Comparable&lt;DoubleIndex&gt; {<a name="line.962"></a>
<FONT color="green">963</FONT>            /** Value to compare. */<a name="line.963"></a>
<FONT color="green">964</FONT>            private final double value;<a name="line.964"></a>
<FONT color="green">965</FONT>            /** Index into sorted array. */<a name="line.965"></a>
<FONT color="green">966</FONT>            private final int index;<a name="line.966"></a>
<FONT color="green">967</FONT>    <a name="line.967"></a>
<FONT color="green">968</FONT>            /**<a name="line.968"></a>
<FONT color="green">969</FONT>             * @param value Value to compare.<a name="line.969"></a>
<FONT color="green">970</FONT>             * @param index Index into sorted array.<a name="line.970"></a>
<FONT color="green">971</FONT>             */<a name="line.971"></a>
<FONT color="green">972</FONT>            DoubleIndex(double value, int index) {<a name="line.972"></a>
<FONT color="green">973</FONT>                this.value = value;<a name="line.973"></a>
<FONT color="green">974</FONT>                this.index = index;<a name="line.974"></a>
<FONT color="green">975</FONT>            }<a name="line.975"></a>
<FONT color="green">976</FONT>    <a name="line.976"></a>
<FONT color="green">977</FONT>            /** {@inheritDoc} */<a name="line.977"></a>
<FONT color="green">978</FONT>            public int compareTo(DoubleIndex o) {<a name="line.978"></a>
<FONT color="green">979</FONT>                return Double.compare(value, o.value);<a name="line.979"></a>
<FONT color="green">980</FONT>            }<a name="line.980"></a>
<FONT color="green">981</FONT>    <a name="line.981"></a>
<FONT color="green">982</FONT>            /** {@inheritDoc} */<a name="line.982"></a>
<FONT color="green">983</FONT>            @Override<a name="line.983"></a>
<FONT color="green">984</FONT>            public boolean equals(Object other) {<a name="line.984"></a>
<FONT color="green">985</FONT>    <a name="line.985"></a>
<FONT color="green">986</FONT>                if (this == other) {<a name="line.986"></a>
<FONT color="green">987</FONT>                    return true;<a name="line.987"></a>
<FONT color="green">988</FONT>                }<a name="line.988"></a>
<FONT color="green">989</FONT>    <a name="line.989"></a>
<FONT color="green">990</FONT>                if (other instanceof DoubleIndex) {<a name="line.990"></a>
<FONT color="green">991</FONT>                    return Double.compare(value, ((DoubleIndex) other).value) == 0;<a name="line.991"></a>
<FONT color="green">992</FONT>                }<a name="line.992"></a>
<FONT color="green">993</FONT>    <a name="line.993"></a>
<FONT color="green">994</FONT>                return false;<a name="line.994"></a>
<FONT color="green">995</FONT>            }<a name="line.995"></a>
<FONT color="green">996</FONT>    <a name="line.996"></a>
<FONT color="green">997</FONT>            /** {@inheritDoc} */<a name="line.997"></a>
<FONT color="green">998</FONT>            @Override<a name="line.998"></a>
<FONT color="green">999</FONT>            public int hashCode() {<a name="line.999"></a>
<FONT color="green">1000</FONT>                long bits = Double.doubleToLongBits(value);<a name="line.1000"></a>
<FONT color="green">1001</FONT>                return (int) ((1438542 ^ (bits &gt;&gt;&gt; 32) ^ bits) &amp; 0xffffffff);<a name="line.1001"></a>
<FONT color="green">1002</FONT>            }<a name="line.1002"></a>
<FONT color="green">1003</FONT>        }<a name="line.1003"></a>
<FONT color="green">1004</FONT>    <a name="line.1004"></a>
<FONT color="green">1005</FONT>        /**<a name="line.1005"></a>
<FONT color="green">1006</FONT>         * Normalizes fitness values to the range [0,1]. Adds a penalty to the<a name="line.1006"></a>
<FONT color="green">1007</FONT>         * fitness value if out of range. The penalty is adjusted by calling<a name="line.1007"></a>
<FONT color="green">1008</FONT>         * setValueRange().<a name="line.1008"></a>
<FONT color="green">1009</FONT>         */<a name="line.1009"></a>
<FONT color="green">1010</FONT>        private class FitnessFunction {<a name="line.1010"></a>
<FONT color="green">1011</FONT>            /** Determines the penalty for boundary violations */<a name="line.1011"></a>
<FONT color="green">1012</FONT>            private double valueRange;<a name="line.1012"></a>
<FONT color="green">1013</FONT>            /**<a name="line.1013"></a>
<FONT color="green">1014</FONT>             * Flag indicating whether the objective variables are forced into their<a name="line.1014"></a>
<FONT color="green">1015</FONT>             * bounds if defined<a name="line.1015"></a>
<FONT color="green">1016</FONT>             */<a name="line.1016"></a>
<FONT color="green">1017</FONT>            private final boolean isRepairMode;<a name="line.1017"></a>
<FONT color="green">1018</FONT>    <a name="line.1018"></a>
<FONT color="green">1019</FONT>            /** Simple constructor.<a name="line.1019"></a>
<FONT color="green">1020</FONT>             */<a name="line.1020"></a>
<FONT color="green">1021</FONT>            public FitnessFunction() {<a name="line.1021"></a>
<FONT color="green">1022</FONT>                valueRange = 1;<a name="line.1022"></a>
<FONT color="green">1023</FONT>                isRepairMode = true;<a name="line.1023"></a>
<FONT color="green">1024</FONT>            }<a name="line.1024"></a>
<FONT color="green">1025</FONT>    <a name="line.1025"></a>
<FONT color="green">1026</FONT>            /**<a name="line.1026"></a>
<FONT color="green">1027</FONT>             * @param point Normalized objective variables.<a name="line.1027"></a>
<FONT color="green">1028</FONT>             * @return the objective value + penalty for violated bounds.<a name="line.1028"></a>
<FONT color="green">1029</FONT>             */<a name="line.1029"></a>
<FONT color="green">1030</FONT>            public double value(final double[] point) {<a name="line.1030"></a>
<FONT color="green">1031</FONT>                double value;<a name="line.1031"></a>
<FONT color="green">1032</FONT>                if (isRepairMode) {<a name="line.1032"></a>
<FONT color="green">1033</FONT>                    double[] repaired = repair(point);<a name="line.1033"></a>
<FONT color="green">1034</FONT>                    value = CMAESOptimizer.this.computeObjectiveValue(repaired) +<a name="line.1034"></a>
<FONT color="green">1035</FONT>                        penalty(point, repaired);<a name="line.1035"></a>
<FONT color="green">1036</FONT>                } else {<a name="line.1036"></a>
<FONT color="green">1037</FONT>                    value = CMAESOptimizer.this.computeObjectiveValue(point);<a name="line.1037"></a>
<FONT color="green">1038</FONT>                }<a name="line.1038"></a>
<FONT color="green">1039</FONT>                return isMinimize ? value : -value;<a name="line.1039"></a>
<FONT color="green">1040</FONT>            }<a name="line.1040"></a>
<FONT color="green">1041</FONT>    <a name="line.1041"></a>
<FONT color="green">1042</FONT>            /**<a name="line.1042"></a>
<FONT color="green">1043</FONT>             * @param x Normalized objective variables.<a name="line.1043"></a>
<FONT color="green">1044</FONT>             * @return {@code true} if in bounds.<a name="line.1044"></a>
<FONT color="green">1045</FONT>             */<a name="line.1045"></a>
<FONT color="green">1046</FONT>            public boolean isFeasible(final double[] x) {<a name="line.1046"></a>
<FONT color="green">1047</FONT>                final double[] lB = CMAESOptimizer.this.getLowerBound();<a name="line.1047"></a>
<FONT color="green">1048</FONT>                final double[] uB = CMAESOptimizer.this.getUpperBound();<a name="line.1048"></a>
<FONT color="green">1049</FONT>    <a name="line.1049"></a>
<FONT color="green">1050</FONT>                for (int i = 0; i &lt; x.length; i++) {<a name="line.1050"></a>
<FONT color="green">1051</FONT>                    if (x[i] &lt; lB[i]) {<a name="line.1051"></a>
<FONT color="green">1052</FONT>                        return false;<a name="line.1052"></a>
<FONT color="green">1053</FONT>                    }<a name="line.1053"></a>
<FONT color="green">1054</FONT>                    if (x[i] &gt; uB[i]) {<a name="line.1054"></a>
<FONT color="green">1055</FONT>                        return false;<a name="line.1055"></a>
<FONT color="green">1056</FONT>                    }<a name="line.1056"></a>
<FONT color="green">1057</FONT>                }<a name="line.1057"></a>
<FONT color="green">1058</FONT>                return true;<a name="line.1058"></a>
<FONT color="green">1059</FONT>            }<a name="line.1059"></a>
<FONT color="green">1060</FONT>    <a name="line.1060"></a>
<FONT color="green">1061</FONT>            /**<a name="line.1061"></a>
<FONT color="green">1062</FONT>             * @param valueRange Adjusts the penalty computation.<a name="line.1062"></a>
<FONT color="green">1063</FONT>             */<a name="line.1063"></a>
<FONT color="green">1064</FONT>            public void setValueRange(double valueRange) {<a name="line.1064"></a>
<FONT color="green">1065</FONT>                this.valueRange = valueRange;<a name="line.1065"></a>
<FONT color="green">1066</FONT>            }<a name="line.1066"></a>
<FONT color="green">1067</FONT>    <a name="line.1067"></a>
<FONT color="green">1068</FONT>            /**<a name="line.1068"></a>
<FONT color="green">1069</FONT>             * @param x Normalized objective variables.<a name="line.1069"></a>
<FONT color="green">1070</FONT>             * @return the repaired (i.e. all in bounds) objective variables.<a name="line.1070"></a>
<FONT color="green">1071</FONT>             */<a name="line.1071"></a>
<FONT color="green">1072</FONT>            private double[] repair(final double[] x) {<a name="line.1072"></a>
<FONT color="green">1073</FONT>                final double[] lB = CMAESOptimizer.this.getLowerBound();<a name="line.1073"></a>
<FONT color="green">1074</FONT>                final double[] uB = CMAESOptimizer.this.getUpperBound();<a name="line.1074"></a>
<FONT color="green">1075</FONT>    <a name="line.1075"></a>
<FONT color="green">1076</FONT>                final double[] repaired = new double[x.length];<a name="line.1076"></a>
<FONT color="green">1077</FONT>                for (int i = 0; i &lt; x.length; i++) {<a name="line.1077"></a>
<FONT color="green">1078</FONT>                    if (x[i] &lt; lB[i]) {<a name="line.1078"></a>
<FONT color="green">1079</FONT>                        repaired[i] = lB[i];<a name="line.1079"></a>
<FONT color="green">1080</FONT>                    } else if (x[i] &gt; uB[i]) {<a name="line.1080"></a>
<FONT color="green">1081</FONT>                        repaired[i] = uB[i];<a name="line.1081"></a>
<FONT color="green">1082</FONT>                    } else {<a name="line.1082"></a>
<FONT color="green">1083</FONT>                        repaired[i] = x[i];<a name="line.1083"></a>
<FONT color="green">1084</FONT>                    }<a name="line.1084"></a>
<FONT color="green">1085</FONT>                }<a name="line.1085"></a>
<FONT color="green">1086</FONT>                return repaired;<a name="line.1086"></a>
<FONT color="green">1087</FONT>            }<a name="line.1087"></a>
<FONT color="green">1088</FONT>    <a name="line.1088"></a>
<FONT color="green">1089</FONT>            /**<a name="line.1089"></a>
<FONT color="green">1090</FONT>             * @param x Normalized objective variables.<a name="line.1090"></a>
<FONT color="green">1091</FONT>             * @param repaired Repaired objective variables.<a name="line.1091"></a>
<FONT color="green">1092</FONT>             * @return Penalty value according to the violation of the bounds.<a name="line.1092"></a>
<FONT color="green">1093</FONT>             */<a name="line.1093"></a>
<FONT color="green">1094</FONT>            private double penalty(final double[] x, final double[] repaired) {<a name="line.1094"></a>
<FONT color="green">1095</FONT>                double penalty = 0;<a name="line.1095"></a>
<FONT color="green">1096</FONT>                for (int i = 0; i &lt; x.length; i++) {<a name="line.1096"></a>
<FONT color="green">1097</FONT>                    double diff = Math.abs(x[i] - repaired[i]);<a name="line.1097"></a>
<FONT color="green">1098</FONT>                    penalty += diff * valueRange;<a name="line.1098"></a>
<FONT color="green">1099</FONT>                }<a name="line.1099"></a>
<FONT color="green">1100</FONT>                return isMinimize ? penalty : -penalty;<a name="line.1100"></a>
<FONT color="green">1101</FONT>            }<a name="line.1101"></a>
<FONT color="green">1102</FONT>        }<a name="line.1102"></a>
<FONT color="green">1103</FONT>    <a name="line.1103"></a>
<FONT color="green">1104</FONT>        // -----Matrix utility functions similar to the Matlab build in functions------<a name="line.1104"></a>
<FONT color="green">1105</FONT>    <a name="line.1105"></a>
<FONT color="green">1106</FONT>        /**<a name="line.1106"></a>
<FONT color="green">1107</FONT>         * @param m Input matrix<a name="line.1107"></a>
<FONT color="green">1108</FONT>         * @return Matrix representing the element-wise logarithm of m.<a name="line.1108"></a>
<FONT color="green">1109</FONT>         */<a name="line.1109"></a>
<FONT color="green">1110</FONT>        private static RealMatrix log(final RealMatrix m) {<a name="line.1110"></a>
<FONT color="green">1111</FONT>            final double[][] d = new double[m.getRowDimension()][m.getColumnDimension()];<a name="line.1111"></a>
<FONT color="green">1112</FONT>            for (int r = 0; r &lt; m.getRowDimension(); r++) {<a name="line.1112"></a>
<FONT color="green">1113</FONT>                for (int c = 0; c &lt; m.getColumnDimension(); c++) {<a name="line.1113"></a>
<FONT color="green">1114</FONT>                    d[r][c] = Math.log(m.getEntry(r, c));<a name="line.1114"></a>
<FONT color="green">1115</FONT>                }<a name="line.1115"></a>
<FONT color="green">1116</FONT>            }<a name="line.1116"></a>
<FONT color="green">1117</FONT>            return new Array2DRowRealMatrix(d, false);<a name="line.1117"></a>
<FONT color="green">1118</FONT>        }<a name="line.1118"></a>
<FONT color="green">1119</FONT>    <a name="line.1119"></a>
<FONT color="green">1120</FONT>        /**<a name="line.1120"></a>
<FONT color="green">1121</FONT>         * @param m Input matrix.<a name="line.1121"></a>
<FONT color="green">1122</FONT>         * @return Matrix representing the element-wise square root of m.<a name="line.1122"></a>
<FONT color="green">1123</FONT>         */<a name="line.1123"></a>
<FONT color="green">1124</FONT>        private static RealMatrix sqrt(final RealMatrix m) {<a name="line.1124"></a>
<FONT color="green">1125</FONT>            final double[][] d = new double[m.getRowDimension()][m.getColumnDimension()];<a name="line.1125"></a>
<FONT color="green">1126</FONT>            for (int r = 0; r &lt; m.getRowDimension(); r++) {<a name="line.1126"></a>
<FONT color="green">1127</FONT>                for (int c = 0; c &lt; m.getColumnDimension(); c++) {<a name="line.1127"></a>
<FONT color="green">1128</FONT>                    d[r][c] = Math.sqrt(m.getEntry(r, c));<a name="line.1128"></a>
<FONT color="green">1129</FONT>                }<a name="line.1129"></a>
<FONT color="green">1130</FONT>            }<a name="line.1130"></a>
<FONT color="green">1131</FONT>            return new Array2DRowRealMatrix(d, false);<a name="line.1131"></a>
<FONT color="green">1132</FONT>        }<a name="line.1132"></a>
<FONT color="green">1133</FONT>    <a name="line.1133"></a>
<FONT color="green">1134</FONT>        /**<a name="line.1134"></a>
<FONT color="green">1135</FONT>         * @param m Input matrix.<a name="line.1135"></a>
<FONT color="green">1136</FONT>         * @return Matrix representing the element-wise square of m.<a name="line.1136"></a>
<FONT color="green">1137</FONT>         */<a name="line.1137"></a>
<FONT color="green">1138</FONT>        private static RealMatrix square(final RealMatrix m) {<a name="line.1138"></a>
<FONT color="green">1139</FONT>            final double[][] d = new double[m.getRowDimension()][m.getColumnDimension()];<a name="line.1139"></a>
<FONT color="green">1140</FONT>            for (int r = 0; r &lt; m.getRowDimension(); r++) {<a name="line.1140"></a>
<FONT color="green">1141</FONT>                for (int c = 0; c &lt; m.getColumnDimension(); c++) {<a name="line.1141"></a>
<FONT color="green">1142</FONT>                    double e = m.getEntry(r, c);<a name="line.1142"></a>
<FONT color="green">1143</FONT>                    d[r][c] = e * e;<a name="line.1143"></a>
<FONT color="green">1144</FONT>                }<a name="line.1144"></a>
<FONT color="green">1145</FONT>            }<a name="line.1145"></a>
<FONT color="green">1146</FONT>            return new Array2DRowRealMatrix(d, false);<a name="line.1146"></a>
<FONT color="green">1147</FONT>        }<a name="line.1147"></a>
<FONT color="green">1148</FONT>    <a name="line.1148"></a>
<FONT color="green">1149</FONT>        /**<a name="line.1149"></a>
<FONT color="green">1150</FONT>         * @param m Input matrix 1.<a name="line.1150"></a>
<FONT color="green">1151</FONT>         * @param n Input matrix 2.<a name="line.1151"></a>
<FONT color="green">1152</FONT>         * @return the matrix where the elements of m and n are element-wise multiplied.<a name="line.1152"></a>
<FONT color="green">1153</FONT>         */<a name="line.1153"></a>
<FONT color="green">1154</FONT>        private static RealMatrix times(final RealMatrix m, final RealMatrix n) {<a name="line.1154"></a>
<FONT color="green">1155</FONT>            final double[][] d = new double[m.getRowDimension()][m.getColumnDimension()];<a name="line.1155"></a>
<FONT color="green">1156</FONT>            for (int r = 0; r &lt; m.getRowDimension(); r++) {<a name="line.1156"></a>
<FONT color="green">1157</FONT>                for (int c = 0; c &lt; m.getColumnDimension(); c++) {<a name="line.1157"></a>
<FONT color="green">1158</FONT>                    d[r][c] = m.getEntry(r, c) * n.getEntry(r, c);<a name="line.1158"></a>
<FONT color="green">1159</FONT>                }<a name="line.1159"></a>
<FONT color="green">1160</FONT>            }<a name="line.1160"></a>
<FONT color="green">1161</FONT>            return new Array2DRowRealMatrix(d, false);<a name="line.1161"></a>
<FONT color="green">1162</FONT>        }<a name="line.1162"></a>
<FONT color="green">1163</FONT>    <a name="line.1163"></a>
<FONT color="green">1164</FONT>        /**<a name="line.1164"></a>
<FONT color="green">1165</FONT>         * @param m Input matrix 1.<a name="line.1165"></a>
<FONT color="green">1166</FONT>         * @param n Input matrix 2.<a name="line.1166"></a>
<FONT color="green">1167</FONT>         * @return Matrix where the elements of m and n are element-wise divided.<a name="line.1167"></a>
<FONT color="green">1168</FONT>         */<a name="line.1168"></a>
<FONT color="green">1169</FONT>        private static RealMatrix divide(final RealMatrix m, final RealMatrix n) {<a name="line.1169"></a>
<FONT color="green">1170</FONT>            final double[][] d = new double[m.getRowDimension()][m.getColumnDimension()];<a name="line.1170"></a>
<FONT color="green">1171</FONT>            for (int r = 0; r &lt; m.getRowDimension(); r++) {<a name="line.1171"></a>
<FONT color="green">1172</FONT>                for (int c = 0; c &lt; m.getColumnDimension(); c++) {<a name="line.1172"></a>
<FONT color="green">1173</FONT>                    d[r][c] = m.getEntry(r, c) / n.getEntry(r, c);<a name="line.1173"></a>
<FONT color="green">1174</FONT>                }<a name="line.1174"></a>
<FONT color="green">1175</FONT>            }<a name="line.1175"></a>
<FONT color="green">1176</FONT>            return new Array2DRowRealMatrix(d, false);<a name="line.1176"></a>
<FONT color="green">1177</FONT>        }<a name="line.1177"></a>
<FONT color="green">1178</FONT>    <a name="line.1178"></a>
<FONT color="green">1179</FONT>        /**<a name="line.1179"></a>
<FONT color="green">1180</FONT>         * @param m Input matrix.<a name="line.1180"></a>
<FONT color="green">1181</FONT>         * @param cols Columns to select.<a name="line.1181"></a>
<FONT color="green">1182</FONT>         * @return Matrix representing the selected columns.<a name="line.1182"></a>
<FONT color="green">1183</FONT>         */<a name="line.1183"></a>
<FONT color="green">1184</FONT>        private static RealMatrix selectColumns(final RealMatrix m, final int[] cols) {<a name="line.1184"></a>
<FONT color="green">1185</FONT>            final double[][] d = new double[m.getRowDimension()][cols.length];<a name="line.1185"></a>
<FONT color="green">1186</FONT>            for (int r = 0; r &lt; m.getRowDimension(); r++) {<a name="line.1186"></a>
<FONT color="green">1187</FONT>                for (int c = 0; c &lt; cols.length; c++) {<a name="line.1187"></a>
<FONT color="green">1188</FONT>                    d[r][c] = m.getEntry(r, cols[c]);<a name="line.1188"></a>
<FONT color="green">1189</FONT>                }<a name="line.1189"></a>
<FONT color="green">1190</FONT>            }<a name="line.1190"></a>
<FONT color="green">1191</FONT>            return new Array2DRowRealMatrix(d, false);<a name="line.1191"></a>
<FONT color="green">1192</FONT>        }<a name="line.1192"></a>
<FONT color="green">1193</FONT>    <a name="line.1193"></a>
<FONT color="green">1194</FONT>        /**<a name="line.1194"></a>
<FONT color="green">1195</FONT>         * @param m Input matrix.<a name="line.1195"></a>
<FONT color="green">1196</FONT>         * @param k Diagonal position.<a name="line.1196"></a>
<FONT color="green">1197</FONT>         * @return Upper triangular part of matrix.<a name="line.1197"></a>
<FONT color="green">1198</FONT>         */<a name="line.1198"></a>
<FONT color="green">1199</FONT>        private static RealMatrix triu(final RealMatrix m, int k) {<a name="line.1199"></a>
<FONT color="green">1200</FONT>            final double[][] d = new double[m.getRowDimension()][m.getColumnDimension()];<a name="line.1200"></a>
<FONT color="green">1201</FONT>            for (int r = 0; r &lt; m.getRowDimension(); r++) {<a name="line.1201"></a>
<FONT color="green">1202</FONT>                for (int c = 0; c &lt; m.getColumnDimension(); c++) {<a name="line.1202"></a>
<FONT color="green">1203</FONT>                    d[r][c] = r &lt;= c - k ? m.getEntry(r, c) : 0;<a name="line.1203"></a>
<FONT color="green">1204</FONT>                }<a name="line.1204"></a>
<FONT color="green">1205</FONT>            }<a name="line.1205"></a>
<FONT color="green">1206</FONT>            return new Array2DRowRealMatrix(d, false);<a name="line.1206"></a>
<FONT color="green">1207</FONT>        }<a name="line.1207"></a>
<FONT color="green">1208</FONT>    <a name="line.1208"></a>
<FONT color="green">1209</FONT>        /**<a name="line.1209"></a>
<FONT color="green">1210</FONT>         * @param m Input matrix.<a name="line.1210"></a>
<FONT color="green">1211</FONT>         * @return Row matrix representing the sums of the rows.<a name="line.1211"></a>
<FONT color="green">1212</FONT>         */<a name="line.1212"></a>
<FONT color="green">1213</FONT>        private static RealMatrix sumRows(final RealMatrix m) {<a name="line.1213"></a>
<FONT color="green">1214</FONT>            final double[][] d = new double[1][m.getColumnDimension()];<a name="line.1214"></a>
<FONT color="green">1215</FONT>            for (int c = 0; c &lt; m.getColumnDimension(); c++) {<a name="line.1215"></a>
<FONT color="green">1216</FONT>                double sum = 0;<a name="line.1216"></a>
<FONT color="green">1217</FONT>                for (int r = 0; r &lt; m.getRowDimension(); r++) {<a name="line.1217"></a>
<FONT color="green">1218</FONT>                    sum += m.getEntry(r, c);<a name="line.1218"></a>
<FONT color="green">1219</FONT>                }<a name="line.1219"></a>
<FONT color="green">1220</FONT>                d[0][c] = sum;<a name="line.1220"></a>
<FONT color="green">1221</FONT>            }<a name="line.1221"></a>
<FONT color="green">1222</FONT>            return new Array2DRowRealMatrix(d, false);<a name="line.1222"></a>
<FONT color="green">1223</FONT>        }<a name="line.1223"></a>
<FONT color="green">1224</FONT>    <a name="line.1224"></a>
<FONT color="green">1225</FONT>        /**<a name="line.1225"></a>
<FONT color="green">1226</FONT>         * @param m Input matrix.<a name="line.1226"></a>
<FONT color="green">1227</FONT>         * @return the diagonal n-by-n matrix if m is a column matrix or the column<a name="line.1227"></a>
<FONT color="green">1228</FONT>         * matrix representing the diagonal if m is a n-by-n matrix.<a name="line.1228"></a>
<FONT color="green">1229</FONT>         */<a name="line.1229"></a>
<FONT color="green">1230</FONT>        private static RealMatrix diag(final RealMatrix m) {<a name="line.1230"></a>
<FONT color="green">1231</FONT>            if (m.getColumnDimension() == 1) {<a name="line.1231"></a>
<FONT color="green">1232</FONT>                final double[][] d = new double[m.getRowDimension()][m.getRowDimension()];<a name="line.1232"></a>
<FONT color="green">1233</FONT>                for (int i = 0; i &lt; m.getRowDimension(); i++) {<a name="line.1233"></a>
<FONT color="green">1234</FONT>                    d[i][i] = m.getEntry(i, 0);<a name="line.1234"></a>
<FONT color="green">1235</FONT>                }<a name="line.1235"></a>
<FONT color="green">1236</FONT>                return new Array2DRowRealMatrix(d, false);<a name="line.1236"></a>
<FONT color="green">1237</FONT>            } else {<a name="line.1237"></a>
<FONT color="green">1238</FONT>                final double[][] d = new double[m.getRowDimension()][1];<a name="line.1238"></a>
<FONT color="green">1239</FONT>                for (int i = 0; i &lt; m.getColumnDimension(); i++) {<a name="line.1239"></a>
<FONT color="green">1240</FONT>                    d[i][0] = m.getEntry(i, i);<a name="line.1240"></a>
<FONT color="green">1241</FONT>                }<a name="line.1241"></a>
<FONT color="green">1242</FONT>                return new Array2DRowRealMatrix(d, false);<a name="line.1242"></a>
<FONT color="green">1243</FONT>            }<a name="line.1243"></a>
<FONT color="green">1244</FONT>        }<a name="line.1244"></a>
<FONT color="green">1245</FONT>    <a name="line.1245"></a>
<FONT color="green">1246</FONT>        /**<a name="line.1246"></a>
<FONT color="green">1247</FONT>         * Copies a column from m1 to m2.<a name="line.1247"></a>
<FONT color="green">1248</FONT>         *<a name="line.1248"></a>
<FONT color="green">1249</FONT>         * @param m1 Source matrix.<a name="line.1249"></a>
<FONT color="green">1250</FONT>         * @param col1 Source column.<a name="line.1250"></a>
<FONT color="green">1251</FONT>         * @param m2 Target matrix.<a name="line.1251"></a>
<FONT color="green">1252</FONT>         * @param col2 Target column.<a name="line.1252"></a>
<FONT color="green">1253</FONT>         */<a name="line.1253"></a>
<FONT color="green">1254</FONT>        private static void copyColumn(final RealMatrix m1, int col1,<a name="line.1254"></a>
<FONT color="green">1255</FONT>                                       RealMatrix m2, int col2) {<a name="line.1255"></a>
<FONT color="green">1256</FONT>            for (int i = 0; i &lt; m1.getRowDimension(); i++) {<a name="line.1256"></a>
<FONT color="green">1257</FONT>                m2.setEntry(i, col2, m1.getEntry(i, col1));<a name="line.1257"></a>
<FONT color="green">1258</FONT>            }<a name="line.1258"></a>
<FONT color="green">1259</FONT>        }<a name="line.1259"></a>
<FONT color="green">1260</FONT>    <a name="line.1260"></a>
<FONT color="green">1261</FONT>        /**<a name="line.1261"></a>
<FONT color="green">1262</FONT>         * @param n Number of rows.<a name="line.1262"></a>
<FONT color="green">1263</FONT>         * @param m Number of columns.<a name="line.1263"></a>
<FONT color="green">1264</FONT>         * @return n-by-m matrix filled with 1.<a name="line.1264"></a>
<FONT color="green">1265</FONT>         */<a name="line.1265"></a>
<FONT color="green">1266</FONT>        private static RealMatrix ones(int n, int m) {<a name="line.1266"></a>
<FONT color="green">1267</FONT>            final double[][] d = new double[n][m];<a name="line.1267"></a>
<FONT color="green">1268</FONT>            for (int r = 0; r &lt; n; r++) {<a name="line.1268"></a>
<FONT color="green">1269</FONT>                Arrays.fill(d[r], 1);<a name="line.1269"></a>
<FONT color="green">1270</FONT>            }<a name="line.1270"></a>
<FONT color="green">1271</FONT>            return new Array2DRowRealMatrix(d, false);<a name="line.1271"></a>
<FONT color="green">1272</FONT>        }<a name="line.1272"></a>
<FONT color="green">1273</FONT>    <a name="line.1273"></a>
<FONT color="green">1274</FONT>        /**<a name="line.1274"></a>
<FONT color="green">1275</FONT>         * @param n Number of rows.<a name="line.1275"></a>
<FONT color="green">1276</FONT>         * @param m Number of columns.<a name="line.1276"></a>
<FONT color="green">1277</FONT>         * @return n-by-m matrix of 0 values out of diagonal, and 1 values on<a name="line.1277"></a>
<FONT color="green">1278</FONT>         * the diagonal.<a name="line.1278"></a>
<FONT color="green">1279</FONT>         */<a name="line.1279"></a>
<FONT color="green">1280</FONT>        private static RealMatrix eye(int n, int m) {<a name="line.1280"></a>
<FONT color="green">1281</FONT>            final double[][] d = new double[n][m];<a name="line.1281"></a>
<FONT color="green">1282</FONT>            for (int r = 0; r &lt; n; r++) {<a name="line.1282"></a>
<FONT color="green">1283</FONT>                if (r &lt; m) {<a name="line.1283"></a>
<FONT color="green">1284</FONT>                    d[r][r] = 1;<a name="line.1284"></a>
<FONT color="green">1285</FONT>                }<a name="line.1285"></a>
<FONT color="green">1286</FONT>            }<a name="line.1286"></a>
<FONT color="green">1287</FONT>            return new Array2DRowRealMatrix(d, false);<a name="line.1287"></a>
<FONT color="green">1288</FONT>        }<a name="line.1288"></a>
<FONT color="green">1289</FONT>    <a name="line.1289"></a>
<FONT color="green">1290</FONT>        /**<a name="line.1290"></a>
<FONT color="green">1291</FONT>         * @param n Number of rows.<a name="line.1291"></a>
<FONT color="green">1292</FONT>         * @param m Number of columns.<a name="line.1292"></a>
<FONT color="green">1293</FONT>         * @return n-by-m matrix of zero values.<a name="line.1293"></a>
<FONT color="green">1294</FONT>         */<a name="line.1294"></a>
<FONT color="green">1295</FONT>        private static RealMatrix zeros(int n, int m) {<a name="line.1295"></a>
<FONT color="green">1296</FONT>            return new Array2DRowRealMatrix(n, m);<a name="line.1296"></a>
<FONT color="green">1297</FONT>        }<a name="line.1297"></a>
<FONT color="green">1298</FONT>    <a name="line.1298"></a>
<FONT color="green">1299</FONT>        /**<a name="line.1299"></a>
<FONT color="green">1300</FONT>         * @param mat Input matrix.<a name="line.1300"></a>
<FONT color="green">1301</FONT>         * @param n Number of row replicates.<a name="line.1301"></a>
<FONT color="green">1302</FONT>         * @param m Number of column replicates.<a name="line.1302"></a>
<FONT color="green">1303</FONT>         * @return a matrix which replicates the input matrix in both directions.<a name="line.1303"></a>
<FONT color="green">1304</FONT>         */<a name="line.1304"></a>
<FONT color="green">1305</FONT>        private static RealMatrix repmat(final RealMatrix mat, int n, int m) {<a name="line.1305"></a>
<FONT color="green">1306</FONT>            final int rd = mat.getRowDimension();<a name="line.1306"></a>
<FONT color="green">1307</FONT>            final int cd = mat.getColumnDimension();<a name="line.1307"></a>
<FONT color="green">1308</FONT>            final double[][] d = new double[n * rd][m * cd];<a name="line.1308"></a>
<FONT color="green">1309</FONT>            for (int r = 0; r &lt; n * rd; r++) {<a name="line.1309"></a>
<FONT color="green">1310</FONT>                for (int c = 0; c &lt; m * cd; c++) {<a name="line.1310"></a>
<FONT color="green">1311</FONT>                    d[r][c] = mat.getEntry(r % rd, c % cd);<a name="line.1311"></a>
<FONT color="green">1312</FONT>                }<a name="line.1312"></a>
<FONT color="green">1313</FONT>            }<a name="line.1313"></a>
<FONT color="green">1314</FONT>            return new Array2DRowRealMatrix(d, false);<a name="line.1314"></a>
<FONT color="green">1315</FONT>        }<a name="line.1315"></a>
<FONT color="green">1316</FONT>    <a name="line.1316"></a>
<FONT color="green">1317</FONT>        /**<a name="line.1317"></a>
<FONT color="green">1318</FONT>         * @param start Start value.<a name="line.1318"></a>
<FONT color="green">1319</FONT>         * @param end End value.<a name="line.1319"></a>
<FONT color="green">1320</FONT>         * @param step Step size.<a name="line.1320"></a>
<FONT color="green">1321</FONT>         * @return a sequence as column matrix.<a name="line.1321"></a>
<FONT color="green">1322</FONT>         */<a name="line.1322"></a>
<FONT color="green">1323</FONT>        private static RealMatrix sequence(double start, double end, double step) {<a name="line.1323"></a>
<FONT color="green">1324</FONT>            final int size = (int) ((end - start) / step + 1);<a name="line.1324"></a>
<FONT color="green">1325</FONT>            final double[][] d = new double[size][1];<a name="line.1325"></a>
<FONT color="green">1326</FONT>            double value = start;<a name="line.1326"></a>
<FONT color="green">1327</FONT>            for (int r = 0; r &lt; size; r++) {<a name="line.1327"></a>
<FONT color="green">1328</FONT>                d[r][0] = value;<a name="line.1328"></a>
<FONT color="green">1329</FONT>                value += step;<a name="line.1329"></a>
<FONT color="green">1330</FONT>            }<a name="line.1330"></a>
<FONT color="green">1331</FONT>            return new Array2DRowRealMatrix(d, false);<a name="line.1331"></a>
<FONT color="green">1332</FONT>        }<a name="line.1332"></a>
<FONT color="green">1333</FONT>    <a name="line.1333"></a>
<FONT color="green">1334</FONT>        /**<a name="line.1334"></a>
<FONT color="green">1335</FONT>         * @param m Input matrix.<a name="line.1335"></a>
<FONT color="green">1336</FONT>         * @return the maximum of the matrix element values.<a name="line.1336"></a>
<FONT color="green">1337</FONT>         */<a name="line.1337"></a>
<FONT color="green">1338</FONT>        private static double max(final RealMatrix m) {<a name="line.1338"></a>
<FONT color="green">1339</FONT>            double max = -Double.MAX_VALUE;<a name="line.1339"></a>
<FONT color="green">1340</FONT>            for (int r = 0; r &lt; m.getRowDimension(); r++) {<a name="line.1340"></a>
<FONT color="green">1341</FONT>                for (int c = 0; c &lt; m.getColumnDimension(); c++) {<a name="line.1341"></a>
<FONT color="green">1342</FONT>                    double e = m.getEntry(r, c);<a name="line.1342"></a>
<FONT color="green">1343</FONT>                    if (max &lt; e) {<a name="line.1343"></a>
<FONT color="green">1344</FONT>                        max = e;<a name="line.1344"></a>
<FONT color="green">1345</FONT>                    }<a name="line.1345"></a>
<FONT color="green">1346</FONT>                }<a name="line.1346"></a>
<FONT color="green">1347</FONT>            }<a name="line.1347"></a>
<FONT color="green">1348</FONT>            return max;<a name="line.1348"></a>
<FONT color="green">1349</FONT>        }<a name="line.1349"></a>
<FONT color="green">1350</FONT>    <a name="line.1350"></a>
<FONT color="green">1351</FONT>        /**<a name="line.1351"></a>
<FONT color="green">1352</FONT>         * @param m Input matrix.<a name="line.1352"></a>
<FONT color="green">1353</FONT>         * @return the minimum of the matrix element values.<a name="line.1353"></a>
<FONT color="green">1354</FONT>         */<a name="line.1354"></a>
<FONT color="green">1355</FONT>        private static double min(final RealMatrix m) {<a name="line.1355"></a>
<FONT color="green">1356</FONT>            double min = Double.MAX_VALUE;<a name="line.1356"></a>
<FONT color="green">1357</FONT>            for (int r = 0; r &lt; m.getRowDimension(); r++) {<a name="line.1357"></a>
<FONT color="green">1358</FONT>                for (int c = 0; c &lt; m.getColumnDimension(); c++) {<a name="line.1358"></a>
<FONT color="green">1359</FONT>                    double e = m.getEntry(r, c);<a name="line.1359"></a>
<FONT color="green">1360</FONT>                    if (min &gt; e) {<a name="line.1360"></a>
<FONT color="green">1361</FONT>                        min = e;<a name="line.1361"></a>
<FONT color="green">1362</FONT>                    }<a name="line.1362"></a>
<FONT color="green">1363</FONT>                }<a name="line.1363"></a>
<FONT color="green">1364</FONT>            }<a name="line.1364"></a>
<FONT color="green">1365</FONT>            return min;<a name="line.1365"></a>
<FONT color="green">1366</FONT>        }<a name="line.1366"></a>
<FONT color="green">1367</FONT>    <a name="line.1367"></a>
<FONT color="green">1368</FONT>        /**<a name="line.1368"></a>
<FONT color="green">1369</FONT>         * @param m Input array.<a name="line.1369"></a>
<FONT color="green">1370</FONT>         * @return the maximum of the array values.<a name="line.1370"></a>
<FONT color="green">1371</FONT>         */<a name="line.1371"></a>
<FONT color="green">1372</FONT>        private static double max(final double[] m) {<a name="line.1372"></a>
<FONT color="green">1373</FONT>            double max = -Double.MAX_VALUE;<a name="line.1373"></a>
<FONT color="green">1374</FONT>            for (int r = 0; r &lt; m.length; r++) {<a name="line.1374"></a>
<FONT color="green">1375</FONT>                if (max &lt; m[r]) {<a name="line.1375"></a>
<FONT color="green">1376</FONT>                    max = m[r];<a name="line.1376"></a>
<FONT color="green">1377</FONT>                }<a name="line.1377"></a>
<FONT color="green">1378</FONT>            }<a name="line.1378"></a>
<FONT color="green">1379</FONT>            return max;<a name="line.1379"></a>
<FONT color="green">1380</FONT>        }<a name="line.1380"></a>
<FONT color="green">1381</FONT>    <a name="line.1381"></a>
<FONT color="green">1382</FONT>        /**<a name="line.1382"></a>
<FONT color="green">1383</FONT>         * @param m Input array.<a name="line.1383"></a>
<FONT color="green">1384</FONT>         * @return the minimum of the array values.<a name="line.1384"></a>
<FONT color="green">1385</FONT>         */<a name="line.1385"></a>
<FONT color="green">1386</FONT>        private static double min(final double[] m) {<a name="line.1386"></a>
<FONT color="green">1387</FONT>            double min = Double.MAX_VALUE;<a name="line.1387"></a>
<FONT color="green">1388</FONT>            for (int r = 0; r &lt; m.length; r++) {<a name="line.1388"></a>
<FONT color="green">1389</FONT>                if (min &gt; m[r]) {<a name="line.1389"></a>
<FONT color="green">1390</FONT>                    min = m[r];<a name="line.1390"></a>
<FONT color="green">1391</FONT>                }<a name="line.1391"></a>
<FONT color="green">1392</FONT>            }<a name="line.1392"></a>
<FONT color="green">1393</FONT>            return min;<a name="line.1393"></a>
<FONT color="green">1394</FONT>        }<a name="line.1394"></a>
<FONT color="green">1395</FONT>    <a name="line.1395"></a>
<FONT color="green">1396</FONT>        /**<a name="line.1396"></a>
<FONT color="green">1397</FONT>         * @param indices Input index array.<a name="line.1397"></a>
<FONT color="green">1398</FONT>         * @return the inverse of the mapping defined by indices.<a name="line.1398"></a>
<FONT color="green">1399</FONT>         */<a name="line.1399"></a>
<FONT color="green">1400</FONT>        private static int[] inverse(final int[] indices) {<a name="line.1400"></a>
<FONT color="green">1401</FONT>            final int[] inverse = new int[indices.length];<a name="line.1401"></a>
<FONT color="green">1402</FONT>            for (int i = 0; i &lt; indices.length; i++) {<a name="line.1402"></a>
<FONT color="green">1403</FONT>                inverse[indices[i]] = i;<a name="line.1403"></a>
<FONT color="green">1404</FONT>            }<a name="line.1404"></a>
<FONT color="green">1405</FONT>            return inverse;<a name="line.1405"></a>
<FONT color="green">1406</FONT>        }<a name="line.1406"></a>
<FONT color="green">1407</FONT>    <a name="line.1407"></a>
<FONT color="green">1408</FONT>        /**<a name="line.1408"></a>
<FONT color="green">1409</FONT>         * @param indices Input index array.<a name="line.1409"></a>
<FONT color="green">1410</FONT>         * @return the indices in inverse order (last is first).<a name="line.1410"></a>
<FONT color="green">1411</FONT>         */<a name="line.1411"></a>
<FONT color="green">1412</FONT>        private static int[] reverse(final int[] indices) {<a name="line.1412"></a>
<FONT color="green">1413</FONT>            final int[] reverse = new int[indices.length];<a name="line.1413"></a>
<FONT color="green">1414</FONT>            for (int i = 0; i &lt; indices.length; i++) {<a name="line.1414"></a>
<FONT color="green">1415</FONT>                reverse[i] = indices[indices.length - i - 1];<a name="line.1415"></a>
<FONT color="green">1416</FONT>            }<a name="line.1416"></a>
<FONT color="green">1417</FONT>            return reverse;<a name="line.1417"></a>
<FONT color="green">1418</FONT>        }<a name="line.1418"></a>
<FONT color="green">1419</FONT>    <a name="line.1419"></a>
<FONT color="green">1420</FONT>        /**<a name="line.1420"></a>
<FONT color="green">1421</FONT>         * @param size Length of random array.<a name="line.1421"></a>
<FONT color="green">1422</FONT>         * @return an array of Gaussian random numbers.<a name="line.1422"></a>
<FONT color="green">1423</FONT>         */<a name="line.1423"></a>
<FONT color="green">1424</FONT>        private double[] randn(int size) {<a name="line.1424"></a>
<FONT color="green">1425</FONT>            final double[] randn = new double[size];<a name="line.1425"></a>
<FONT color="green">1426</FONT>            for (int i = 0; i &lt; size; i++) {<a name="line.1426"></a>
<FONT color="green">1427</FONT>                randn[i] = random.nextGaussian();<a name="line.1427"></a>
<FONT color="green">1428</FONT>            }<a name="line.1428"></a>
<FONT color="green">1429</FONT>            return randn;<a name="line.1429"></a>
<FONT color="green">1430</FONT>        }<a name="line.1430"></a>
<FONT color="green">1431</FONT>    <a name="line.1431"></a>
<FONT color="green">1432</FONT>        /**<a name="line.1432"></a>
<FONT color="green">1433</FONT>         * @param size Number of rows.<a name="line.1433"></a>
<FONT color="green">1434</FONT>         * @param popSize Population size.<a name="line.1434"></a>
<FONT color="green">1435</FONT>         * @return a 2-dimensional matrix of Gaussian random numbers.<a name="line.1435"></a>
<FONT color="green">1436</FONT>         */<a name="line.1436"></a>
<FONT color="green">1437</FONT>        private RealMatrix randn1(int size, int popSize) {<a name="line.1437"></a>
<FONT color="green">1438</FONT>            final double[][] d = new double[size][popSize];<a name="line.1438"></a>
<FONT color="green">1439</FONT>            for (int r = 0; r &lt; size; r++) {<a name="line.1439"></a>
<FONT color="green">1440</FONT>                for (int c = 0; c &lt; popSize; c++) {<a name="line.1440"></a>
<FONT color="green">1441</FONT>                    d[r][c] = random.nextGaussian();<a name="line.1441"></a>
<FONT color="green">1442</FONT>                }<a name="line.1442"></a>
<FONT color="green">1443</FONT>            }<a name="line.1443"></a>
<FONT color="green">1444</FONT>            return new Array2DRowRealMatrix(d, false);<a name="line.1444"></a>
<FONT color="green">1445</FONT>        }<a name="line.1445"></a>
<FONT color="green">1446</FONT>    }<a name="line.1446"></a>




























































</PRE>
</BODY>
</HTML>
